Recent zbMATH articles in MSC 62Fhttps://zbmath.org/atom/cc/62F2024-03-13T18:33:02.981707ZWerkzeugOn quantile-based asymmetric family of distributions: properties and inferencehttps://zbmath.org/1528.600182024-03-13T18:33:02.981707Z"Gijbels, Irène"https://zbmath.org/authors/?q=ai:gijbels.irene"Karim, Rezaul"https://zbmath.org/authors/?q=ai:karim.rezaul"Verhasselt, Anneleen"https://zbmath.org/authors/?q=ai:verhasselt.anneleenSummary: In this paper, we provide a detailed study of a general family of asymmetric densities. In the general framework, we establish expressions for important characteristics of the distributions and discuss estimation of the parameters via method-of-moments as well as maximum likelihood estimation. Asymptotic normality results for the estimators are provided. The results under the general framework are then applied to some specific examples of asymmetric densities. The use of the asymmetric densities is illustrated in a real-data analysis.
{{\copyright} 2019 The Authors. International Statistical Review {\copyright} 2019 International Statistical Institute}Response to the letter to the editor on ``On quantile-based asymmetric family of distributions: properties and inference''https://zbmath.org/1528.600192024-03-13T18:33:02.981707Z"Gijbels, Irène"https://zbmath.org/authors/?q=ai:gijbels.irene"Karim, Rezaul"https://zbmath.org/authors/?q=ai:karim.rezaul"Verhasselt, Anneleen"https://zbmath.org/authors/?q=ai:verhasselt.anneleenSummary: \textit{F. J. R. Alvarez} [Int. Stat. Rev. 88, No. 3, 793--796 (2020; Zbl 1528.60021)] points out an identification problem for the four-parameter family of two-piece asymmetric densities introduced by \textit{V. Nassiri} and \textit{I. Loris} [J. Appl. Stat. 40, No. 5, 1090--1105 (2013; Zbl 1514.62770)]. This implies that statistical inference for that family is problematic. Establishing probabilistic properties for this four-parameter family however still makes sense. For the three-parameter family, there is no identification problem. The main contribution in [the authors, ibid. 87, No. 3, 471--504 (2019; Zbl 1528.60018)] is to provide asymptotic results for maximum likelihood and method-of-moments estimators for members of the three-parameter quantile-based asymmetric family of distributions.
{{\copyright} 2020 International Statistical Institute}Letter to the editor: ``On quantile-based asymmetric family of distributions: properties and inference''https://zbmath.org/1528.600212024-03-13T18:33:02.981707Z"Rubio Alvarez, Francisco J."https://zbmath.org/authors/?q=ai:alvarez.francisco-j-rubioSummary: We show that the family of asymmetric distributions studied in a recent publication in the International Statistical Review is equivalent to the family of two-piece distributions. Moreover, we show that the location-scale asymmetric family proposed in that publication is non-identifiable (overparameterised), and it coincides with the family of two-piece distributions after removing the redundant parameters.
{{\copyright} 2020 International Statistical Institute}
Comment to the paper [\textit{I. Gijbels} et al., Int. Stat. Rev. 87, No. 3, 471--504 (2019; Zbl 1528.60018)].Smoothing and benchmarking for small area estimationhttps://zbmath.org/1528.620092024-03-13T18:33:02.981707Z"Steorts, Rebecca C."https://zbmath.org/authors/?q=ai:steorts.rebecca-c"Schmid, Timo"https://zbmath.org/authors/?q=ai:schmid.timo"Tzavidis, Nikos"https://zbmath.org/authors/?q=ai:tzavidis.nikosSummary: Small area estimation is concerned with methodology for estimating population parameters associated with a geographic area defined by a cross-classification that may also include non-geographic dimensions. In this paper, we develop constrained estimation methods for small area problems: those requiring smoothness with respect to similarity across areas, such as geographic proximity or clustering by covariates, and benchmarking constraints, requiring weighted means of estimates to agree across levels of aggregation. We develop methods for constrained estimation decision theoretically and discuss their geometric interpretation. The constrained estimators are the solutions to tractable optimisation problems and have closed-form solutions. Mean squared errors of the constrained estimators are calculated via bootstrapping. Our approach assumes the Bayes estimator exists and is applicable to any proposed model. In addition, we give special cases of our techniques under certain distributional assumptions. We illustrate the proposed methodology using web-scraped data on Berlin rents aggregated over areas to ensure privacy.
{{\copyright} 2020 The Authors. International Statistical Review {\copyright} 2020 International Statistical Institute}Optimal non-adaptive probabilistic group testing in general sparsity regimeshttps://zbmath.org/1528.620122024-03-13T18:33:02.981707Z"Bay, Wei Heng"https://zbmath.org/authors/?q=ai:bay.wei-heng"Scarlett, Jonathan"https://zbmath.org/authors/?q=ai:scarlett.jonathan"Price, Eric"https://zbmath.org/authors/?q=ai:price.ericSummary: In this paper, we consider the problem of noiseless non-adaptive probabilistic group testing, in which the goal is high-probability recovery of the defective set. We show that in the case of \(n\) items among which \(k\) are defective, the smallest possible number of tests equals \(\min\{C_{k, n} k\log n, n\}\) up to lower-order asymptotic terms, where \(C_{k, n}\) is a uniformly bounded constant (varying depending on the scaling of \(k\) with respect to \(n\)) with a simple explicit expression. The algorithmic upper bound follows from a minor adaptation of an existing analysis of the Definite Defectives algorithm, and the algorithm-independent lower bound builds on existing works for the regimes \(k\leq n^{1-\varOmega(1)}\) and \(k = \varTheta(n)\). In sufficiently sparse regimes (including \(k = o\left(\frac{n}{\log n}\right))\), our main result generalizes that of \textit{A. Coja-Oghlan} et al. [Comb. Probab. Comput. 30, No. 6, 811--848 (2021; Zbl 1511.92030)] by avoiding the assumption \(k\leq n^{1-\varOmega(1)}\), whereas in sufficiently dense regimes (including \(k = \omega\left(\frac{n}{\log n}\right)\)), our main result shows that individual testing is asymptotically optimal for any non-zero target success probability, thus strengthening an existing result of \textit{M. Aldridge} [IEEE Trans. Inf. Theory 65, No. 4, 2058--2061 (2019; Zbl 1432.62036)] in terms of both the error probability and the assumed scaling of \(k\).Small-sample testing inference in symmetric and log-symmetric linear regression modelshttps://zbmath.org/1528.620132024-03-13T18:33:02.981707Z"Medeiros, Francisco M. C."https://zbmath.org/authors/?q=ai:medeiros.francisco-m-c"Ferrari, Silvia L. P."https://zbmath.org/authors/?q=ai:ferrari.silvia-l-de-paulaSummary: This paper deals with the issue of testing hypotheses in symmetric and log-symmetric linear regression models in small and moderate-sized samples. We focus on four tests, namely, the Wald, likelihood ratio, score, and gradient tests. These tests rely on asymptotic results and are unreliable when the sample size is not large enough to guarantee a good agreement between the exact distribution of the test statistic and the corresponding chi-squared asymptotic distribution. Bartlett and Bartlett-type corrections typically attenuate the size distortion of the tests. These corrections are available in the literature for the likelihood ratio and score tests in symmetric linear regression models. Here, we derive a Bartlett-type correction for the gradient test. We show that the corrections are also valid for the log-symmetric linear regression models. We numerically compare the various tests and bootstrapped tests, through simulations. Our results suggest that the corrected and bootstrapped tests exhibit type I probability error closer to the chosen nominal level with virtually no power loss. The analytically corrected tests as well as the bootstrapped tests, including the Bartlett-corrected gradient test derived in this paper, perform with the advantage of not requiring computationally intensive calculations. We present a real data application to illustrate the usefulness of the modified tests.
{{\copyright} 2017 The Authors. Statistica Neerlandica {\copyright} 2017 VVS.}Moment-based estimation for parameters of general inverse subordinatorhttps://zbmath.org/1528.620142024-03-13T18:33:02.981707Z"Grzesiek, Aleksandra"https://zbmath.org/authors/?q=ai:grzesiek.aleksandra"Połoczański, Rafał"https://zbmath.org/authors/?q=ai:poloczanski.rafal"Kumar, Arun"https://zbmath.org/authors/?q=ai:kumar.arun.1"Wyłomańska, Agnieszka"https://zbmath.org/authors/?q=ai:wylomanska.agnieszkaSummary: In recent years the processes with anomalous diffusive dynamics have been widely discussed in the literature. The classic example of the anomalous diffusive models is the continuous time random walk (CTRW) which is a natural generalization of the random walk model. One of the fundamental properties of the classical CTRW is the fact that in the limit it tends to the Brownian motion subordinated by the so-called \(\beta\)-stable subordinator when the mean of waiting times is infinite. One can consider the generalization of such subordinated model by taking general inverse subordinator instead of the \(\beta\)-stable one as a time-change. The inverse subordinator is the first exit time of the non-decreasing Lévy process also called subordinator. In this paper we consider the Brownian motion delayed by general inverse subordinator. The main attention is paid to the estimation method of the parameters of the general inverse subordinator in the considered model. We propose a novel estimation technique based on the discretization of the subordinator's distribution. Using this approach we demonstrate that the distribution of the constant time periods, visible in the trajectory of the considered model, can be described by the so-called modified cumulative distribution function. This paper is an extension of the authors' previous article where a similar approach was applied, however here we focus on moment-based estimation and compare it with other popular methods of estimation. The effectiveness of the new algorithm is verified using the Monte Carlo approach.On solving bias-corrected non-linear estimation equations with an application to the dynamic linear modelhttps://zbmath.org/1528.620152024-03-13T18:33:02.981707Z"Mahmood, Munir"https://zbmath.org/authors/?q=ai:mahmood.munir"King, Maxwell L."https://zbmath.org/authors/?q=ai:king.maxwell-lSummary: In a seminal paper, \textit{T. K. Mak} [J. R. Stat. Soc., Ser. B 55, No. 4, 945--955 (1993; Zbl 0782.62030)] derived an efficient algorithm for solving non-linear unbiased estimation equations. In this paper, we show that when Mak's algorithm is applied to biased estimation equations, it results in the estimates that would come from solving a bias-corrected estimation equation, making it a consistent estimator if regularity conditions hold. In addition, the properties that Mak established for his algorithm also apply in the case of biased estimation equations but for estimates from the bias-corrected equations. The marginal likelihood estimator is obtained when the approach is applied to both maximum likelihood and least squares estimation of the covariance matrix parameters in the general linear regression model. The new approach results in two new estimators when applied to the profile and marginal likelihood functions for estimating the lagged dependent variable coefficient in the dynamic linear regression model. Monte Carlo simulation results show the new approach leads to a better estimator when applied to the standard profile likelihood. It is therefore recommended for situations in which standard estimators are known to be biased.
{{\copyright} 2016 The Authors. Statistica Neerlandica {\copyright} 2016 VVS.}Bayesian robustness modelling using the \(O\)-regularly varying distributionshttps://zbmath.org/1528.620162024-03-13T18:33:02.981707Z"Andrade, J. A. A."https://zbmath.org/authors/?q=ai:andrade.jose-ailton-alencar"Omey, Edward"https://zbmath.org/authors/?q=ai:omey.edwardSummary: The theory of robustness modelling is essentially based on heavy-tailed distributions, because longer tails are more prepared to deal with diverse information (such as outliers) because of the higher probabilities on the tails. There are many classes of distributions that can be regarded as heavy tails; some of them have interesting properties and are not explored in statistics. In the present work, we propose a robustness modelling approach based on the \(O\)-regularly varying class (ORV), which is a generalization of the regular variation family; however, the ORV class allows more flexible tails behaviour, which can improve the way in which the outlying information is discarded by the model. We establish sufficient conditions in the location and in the scale parameter structures, which allow to resolve automatically the conflicts of information. We also provide a procedure for generating new distributions within the ORV class.
{{\copyright} 2017 The Authors. Statistica Neerlandica {\copyright} 2017 VVS.}Likelihood, replicability and Robbins' confidence sequenceshttps://zbmath.org/1528.620172024-03-13T18:33:02.981707Z"Pace, Luigi"https://zbmath.org/authors/?q=ai:pace.luigi"Salvan, Alessandra"https://zbmath.org/authors/?q=ai:salvan.alessandraSummary: The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have produced the data at hand, rely on a feeble concept of replicability. In particular, contradictory conclusions may be reached when a substantial enlargement of the study is undertaken. To redefine statistical confidence in such a way that inferential conclusions are non-contradictory, with large enough probability, under enlargements of the sample, we give a new reading of a proposal dating back to the 60s, namely, Robbins' confidence sequences. Directly bounding the probability of reaching, in the future, conclusions that contradict the current ones, Robbins' confidence sequences ensure a clear-cut form of replicability when inference is performed on accumulating data. Their main frequentist property is easy to understand and to prove. We show that Robbins' confidence sequences may be justified under various views of inference: they are likelihood-based, can incorporate prior information and obey the strong likelihood principle. They are easy to compute, even when inference is on a parameter of interest, especially using a closed form approximation from normal asymptotic theory.
{{\copyright} 2019 The Authors. International Statistical Review {\copyright} 2019 International Statistical Institute}Robust maximum likelihood estimationhttps://zbmath.org/1528.620182024-03-13T18:33:02.981707Z"Bertsimas, Dimitris"https://zbmath.org/authors/?q=ai:bertsimas.dimitris-j"Nohadani, Omid"https://zbmath.org/authors/?q=ai:nohadani.omidSummary: In many applications, statistical estimators serve to derive conclusions from data, for example, in finance, medical decision making, and clinical trials. However, the conclusions are typically dependent on uncertainties in the data. We use robust optimization principles to provide robust maximum likelihood estimators that are protected against data errors. Both types of input data errors are considered: (a) the adversarial type, modeled using the notion of uncertainty sets, and (b) the probabilistic type, modeled by distributions. We provide efficient local and global search algorithms to compute the robust estimators and discuss them in detail for the case of multivariate normally distributed data. The estimator performance is demonstrated on two applications. First, using computer simulations, we demonstrate that the proposed estimators are robust against both types of data uncertainty and provide more accurate estimates compared with classical estimators, which degrade significantly, when errors are encountered. We establish a range of uncertainty sizes for which robust estimators are superior. Second, we analyze deviations in cancer radiation therapy planning. Uncertainties among plans are caused by patients' individual anatomies and the trial-and-error nature of the process. When analyzing a large set of past clinical treatment data, robust estimators lead to more reliable decisions when applied to a large set of past treatment plans.On the robustness to adversarial corruption and to heavy-tailed data of the Stahel-Donoho median of meanshttps://zbmath.org/1528.620192024-03-13T18:33:02.981707Z"Depersin, Jules"https://zbmath.org/authors/?q=ai:depersin.jules"Lecué, Guillaume"https://zbmath.org/authors/?q=ai:lecue.guillaumeSummary: We consider median of means (MOM) versions of the Stahel-Donoho outlyingness (SDO) [\textit{D. L. Donoho}, ``Breakdown properties of multivariate location estimators'', Techn. Rep., Harvard Univ. (1982); \textit{W. A. Stahel}, Robuste Schätzungen: Infinitesimale Optimalität und Schätzungen von Kovarianzmatrizen. Zürich: Eidgenössische Technische Hochschule Zürich (Diss.) (1981; Zbl 0531.62036)] and of the Median Absolute Deviation (MAD) [\textit{F. R. Hampel}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 27, 87--104 (1973; Zbl 0255.62045)] functions to construct subgaussian estimators of a mean vector under adversarial contamination and heavy-tailed data. We develop a single analysis of the MOM version of the SDO which covers all cases ranging from the Gaussian case to the \(L_2\) case. It is based on isomorphic and almost isometric properties of the MOM versions of SDO and MAD. This analysis also covers cases where the mean does not even exist but a location parameter does; in those cases we still recover the same subgaussian rates and the same price for adversarial contamination even though there is not even a first moment. These properties are achieved by the classical SDO median and are therefore the first non-asymptotic statistical bounds on the Stahel-Donoho median complementing the \(\sqrt{n}\)-consistency [\textit{R. A. Maronna} and \textit{V. J. Yohai}, J. Am. Stat. Assoc. 90, No. 429, 330--341 (1995; Zbl 0820.62050)] and asymptotic normality [\textit{Y. Zuo} et al., Ann. Stat. 32, No. 1, 167--188 (2004; Zbl 1105.62349)] of the Stahel-Donoho estimators. We also show that the MOM version of MAD can be used to construct an estimator of the covariance matrix only under the existence of a second moment or of a scatter matrix if a second moment does not exist.Statistical inference on restricted partial linear regression models with partial distortion measurement errorshttps://zbmath.org/1528.620242024-03-13T18:33:02.981707Z"Zhang, Jun"https://zbmath.org/authors/?q=ai:zhang.jun.10"Zhou, Nanguang"https://zbmath.org/authors/?q=ai:zhou.nanguang"Sun, Zipeng"https://zbmath.org/authors/?q=ai:sun.zipeng"Li, Gaorong"https://zbmath.org/authors/?q=ai:li.gaorong"Wei, Zhenghong"https://zbmath.org/authors/?q=ai:wei.zhenghongSummary: We consider the estimation and hypothesis testing problems for the partial linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variable. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. To test a hypothesis on the parametric components, a restricted least squares estimator is proposed under the null hypothesis. Asymptotic properties for the estimators are established. A test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we also obtain the asymptotic properties of the test statistic. A wild bootstrap procedure is proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure, and a real example is analyzed for an illustration.
{{\copyright} 2016 The Authors. Statistica Neerlandica {\copyright} 2016 VVS.}Unsupervised feature selection via data reconstruction and side informationhttps://zbmath.org/1528.620282024-03-13T18:33:02.981707Z"Zhang, Rui"https://zbmath.org/authors/?q=ai:zhang.rui.23"Li, Xuelong"https://zbmath.org/authors/?q=ai:li.xuelongEditorial remark: No review copy delivered.Bayesian model selection of Gaussian directed acyclic graph structureshttps://zbmath.org/1528.620302024-03-13T18:33:02.981707Z"Castelletti, Federico"https://zbmath.org/authors/?q=ai:castelletti.federicoSummary: During the last years, graphical models have become a popular tool to represent dependencies among variables in many scientific areas. Typically, the objective is to dependence relationships that can be represented through a directed acyclic graph (DAG). The set of all conditional independencies encoded by a DAG determines its Markov property. In general, DAGs encoding the same conditional independencies are not distinguishable from observational data and can be collected into equivalence classes, each one represented by a chain graph called essential graph (EG). However, both the DAG and EG space grow super exponentially in the number of variables, and so, graph structural learning requires the adoption of Markov chain Monte Carlo (MCMC) techniques. In this paper, we review some recent results on Bayesian model selection of Gaussian DAG models under a unified framework. These results are based on closed-form expressions for the marginal likelihood of a DAG and EG structure, which is obtained from a few suitable assumptions on the prior for model parameters. We then introduce a general MCMC scheme that can be adopted both for model selection of DAGs and EGs together with a couple of applications on real data sets.
{{\copyright} 2020 International Statistical Institute.}Multiple testing and variable selection along the path of the least angle regressionhttps://zbmath.org/1528.620402024-03-13T18:33:02.981707Z"Azaïs, Jean-Marc"https://zbmath.org/authors/?q=ai:azais.jean-marc"De Castro, Yohann"https://zbmath.org/authors/?q=ai:de-castro.yohannSummary: We investigate multiple testing and variable selection using the Least Angle Regression (LARS) algorithm in high dimensions under the assumption of Gaussian noise. LARS is known to produce a piecewise affine solution path with change points referred to as the \textit{knots of the LARS path}. The key to our results is an expression in closed form of the exact joint law of a \(K\)-tuple of knots conditional on the variables selected by LARS, the so-called \textit{post-selection} joint law of the LARS knots. Numerical experiments demonstrate the perfect fit of our findings. This paper makes three main contributions. First, we build testing procedures on variables entering the model along the LARS path in the general design case when the noise level can be unknown. These testing procedures are referred to as the Generalized \(t\)-Spacing tests and we prove that they have an exact non-asymptotic level (i.e. the Type I error is exactly controlled). This extends work of \textit{R. J. Tibshirani} et al. [J. Am. Stat. Assoc. 111, No. 514, 600--620 (2016; \url{doi:10.1080/01621459.2015.1108848})] where the spacing test works for consecutive knots and known variance. Second, we introduce a new exact multiple testing procedure after model selection in the general design case when the noise level may be unknown. We prove that this testing procedure has exact non-asymptotic level for general design and unknown noise level. Third, we prove exact control of the false discovery rate under orthogonal design assumption. Monte-Carlo simulations and a real data experiment are provided to illustrate our results in this case. Of independent interest, we introduce an equivalent formulation of the LARS algorithm based on a recursive function.A negative binomial autoregression with a linear conditional variance-to-mean functionhttps://zbmath.org/1528.620422024-03-13T18:33:02.981707Z"Almohaimeed, Bader S."https://zbmath.org/authors/?q=ai:almohaimeed.bader-sSummary: A general integer-valued time-series model with a conditional variance proportional to the conditional mean is proposed. Specifically, the conditional distribution is a Poisson mixture with a dependent mixing sequence, which results in a negative binomial distribution with a linear conditional variance-to-mean relationship. In addition, the conditional mean is specified as a general parametric function of past observations. We first propose stationarity, ergodicity, and finite moment conditions for the model. Furthermore, the parameters are estimated using the Poisson quasi-maximum likelihood estimate, whose asymptotic properties are studied under weak conditions. Illustrations of the proposed methodology on simulated and actual time series of counts are given.Poisson-geometric INAR(1) process for modeling count time series with overdispersionhttps://zbmath.org/1528.620432024-03-13T18:33:02.981707Z"Bourguignon, Marcelo"https://zbmath.org/authors/?q=ai:bourguignon.marceloSummary: In this paper, we propose a new first-order non-negative integer-valued autoregressive [INAR(1)] process with Poisson-geometric marginals based on binomial thinning for modeling integer-valued time series with overdispersion. Also, the new process has, as a particular case, the Poisson INAR(1) and geometric INAR(1) processes. The main properties of the model are derived, such as probability generating function, moments, conditional distribution, higher-order moments, and jumps. Estimators for the parameters of process are proposed, and their asymptotic properties are established. Some numerical results of the estimators are presented with a discussion of the obtained results. Applications to two real data sets are given to show the potentiality of the new process.
{{\copyright} 2015 The Author. Statistica Neerlandica {\copyright} 2015 VVS.}Markov switching quantile autoregressionhttps://zbmath.org/1528.620452024-03-13T18:33:02.981707Z"Liu, Xiaochun"https://zbmath.org/authors/?q=ai:liu.xiaochunSummary: This paper considers the location-scale quantile autoregression in which the location and scale parameters are subject to regime shifts. The regime changes in lower and upper tails are determined by the outcome of a latent, discrete-state Markov process. The new method provides direct inference and estimate for different parts of a non-stationary time series distribution. Bayesian inference for switching regimes within a quantile, via a three-parameter asymmetric Laplace distribution, is adapted and designed for parameter estimation. Using the Bayesian output, the marginal likelihood is readily available for testing the presence and the number of regimes. The simulation study shows that the predictability of regimes and conditional quantiles by using asymmetric Laplace distribution as the likelihood is fairly comparable with the true model distributions. However, ignoring that autoregressive coefficients might be quantile dependent leads to substantial bias in both regime inference and quantile prediction. The potential of this new approach is illustrated in the empirical applications to the US inflation and real exchange rates for asymmetric dynamics and the S\&P 500 index returns of different frequencies for financial market risk assessment.
{{\copyright} 2016 The Authors. Statistica Neerlandica {\copyright} 2016 VVS.}Performance measures in dose-finding experimentshttps://zbmath.org/1528.620652024-03-13T18:33:02.981707Z"Flournoy, Nancy"https://zbmath.org/authors/?q=ai:flournoy.nancy"Moler, José"https://zbmath.org/authors/?q=ai:moler.jose-antonio"Plo, Fernando"https://zbmath.org/authors/?q=ai:plo.fernandoSummary: In the first phase of pharmaceutical development, and assuming that the probability of positive response increases with dose, the main statistical goal is to estimate a percentile of the dose-response function for a given target value \(\Gamma\). We compare the Maximum Likelihood and centred isotonic regression estimators of the target dose and we discuss several performance criteria to assess inferential precision, the amount of toxicity exposure and the trade-off between them for a set of some exemplary adaptive designs. We compare these designs using graphical tools. Several scenarios are considered using simulation, including the use of several start-up rules, the change of slope of the dose-toxicity function at the target dose and also different theoretical models, as logistic, normal or skew-normal distribution functions.
{{\copyright} 2020 The Authors. International Statistical Review published by John Wiley \& Sons Ltd on behalf of International Statistical Institute.}Conditional assessment of the impact of a Hausman pretest on confidence intervalshttps://zbmath.org/1528.620842024-03-13T18:33:02.981707Z"Kabaila, Paul"https://zbmath.org/authors/?q=ai:kabaila.paul-v"Mainzer, Rheanna"https://zbmath.org/authors/?q=ai:mainzer.rheanna"Farchione, Davide"https://zbmath.org/authors/?q=ai:farchione.davideSummary: In the analysis of clustered and longitudinal data, which includes a covariate that varies both between and within clusters, a Hausman pretest is commonly used to decide whether subsequent inference is made using the linear random intercept model or the fixed effects model. We assess the effect of this pretest on the coverage probability and expected length of a confidence interval for the slope, conditional on the observed values of the covariate. This assessment has the advantages that it (i) relates to the values of this covariate at hand, (ii) is valid irrespective of how this covariate is generated, (iii) uses exact finite sample results, and (iv) results in an assessment that is determined by the values of this covariate and only two unknown parameters. For two real data sets, our conditional analysis shows that the confidence interval constructed after a Hausman pretest should not be used.
{{\copyright} 2017 The Authors. Statistica Neerlandica {\copyright} 2017 VVS.}Bayesian approach to LR assessment in case of rare type matchhttps://zbmath.org/1528.620892024-03-13T18:33:02.981707Z"Cereda, Giulia"https://zbmath.org/authors/?q=ai:cereda.giuliaSummary: The likelihood ratio (LR) is largely used to evaluate the relative weight of forensic data regarding two hypotheses, and for its assessment, Bayesian methods are widespread in the forensic field. However, the Bayesian `recipe' for the LR presented in most of the literature consists of plugging-in Bayesian estimates of the involved nuisance parameters into a frequentist-defined LR: frequentist and Bayesian methods are thus mixed, giving rise to solutions obtained by hybrid reasoning. This paper provides the derivation of a proper Bayesian approach to assess LRs for the `rare type match problem', the situation in which the expert wants to evaluate a match between the DNA profile of a suspect and that of a trace from the crime scene, and this profile has never been observed before in the database of reference. LR assessment using the two most popular Bayesian models (beta-binomial and Dirichlet-multinomial) is discussed and compared with corresponding plug-in versions.
{{\copyright} 2017 The Author. Statistica Neerlandica {\copyright} 2017 VVS.}An application of the generalized Poisson difference distribution to the Bayesian modelling of football scoreshttps://zbmath.org/1528.620902024-03-13T18:33:02.981707Z"Shahtahmassebi, Golnaz"https://zbmath.org/authors/?q=ai:shahtahmassebi.golnaz"Moyeed, Rana"https://zbmath.org/authors/?q=ai:moyeed.rana-aSummary: The analysis of sports data, in particular football match outcomes, has always produced an immense interest among the statisticians. In this paper, we adopt the generalized Poisson difference distribution (GPDD) to model the goal difference of football matches. We discuss the advantages of the proposed model over the Poisson difference (PD) model, which was also used for the same purpose. The GPDD model, like the PD model, is based on the goal difference in each game that allows us to account for the correlation without explicitly modelling it. The main advantage of the GPDD model is its flexibility in the tails by considering shorter as well as longer tails than the PD distribution. We carry out the analysis in a Bayesian framework in order to incorporate external information, such as historical knowledge or data, through the prior distributions. We model both the mean and the variance of the goal difference and show that such a model performs considerably better than a model with a fixed variance. Finally, the proposed model is fitted to the 2012--2013 Italian Serie A football data, and various model diagnostics are carried out to evaluate the performance of the model.
{{\copyright} 2016 The Authors. Statistica Neerlandica {\copyright} 2016 VVS.}Tests of normality of functional datahttps://zbmath.org/1528.620912024-03-13T18:33:02.981707Z"Górecki, Tomasz"https://zbmath.org/authors/?q=ai:gorecki.tomasz-t"Horváth, Lajos"https://zbmath.org/authors/?q=ai:horvath.lajos"Kokoszka, Piotr"https://zbmath.org/authors/?q=ai:kokoszka.piotr-sSummary: The paper is concerned with testing normality in samples of curves and error curves estimated from functional regression models. We propose a general paradigm based on the application of multivariate normality tests to vectors of functional principal components scores. We examine finite sample performance of a number of such tests and select the best performing tests. We apply them to several extensively used functional data sets and determine which can be treated as normal, possibly after a suitable transformation. We also offer practical guidance on software implementations of all tests we study and develop large sample justification for tests based on sample skewness and kurtosis of functional principal component scores.
{{\copyright} 2020 The Authors. International Statistical Review {\copyright} 2020 International Statistical Institute}DAFI: an open-source framework for ensemble-based data assimilation and field inversionhttps://zbmath.org/1528.650642024-03-13T18:33:02.981707Z"Michelén Ströfer, Carlos A."https://zbmath.org/authors/?q=ai:michelen-strofer.carlos-a"Zhang, Xin-Lei"https://zbmath.org/authors/?q=ai:zhang.xinlei"Xiao, Heng"https://zbmath.org/authors/?q=ai:xiao.hengSummary: In many areas of science and engineering, it is a common task to infer physical fields from sparse observations. This paper presents the DAFI code intended as a flexible framework for two broad classes of such inverse problems: data assimilation and field inversion. DAFI generalizes these diverse problems into a general formulation and solves it with ensemble Kalman filters, a family of ensemble-based, derivative-free, Bayesian methods. This Bayesian approach has the added advantage of providing built-in uncertainty quantification. Moreover, the code provides tools for performing common tasks related to random fields, as well as I/O utilities for integration with the open-source finite volume tool OpenFOAM. The code capabilities are showcased through several test cases including state and parameter estimation for the Lorenz dynamic system, field inversion for the diffusion equations, and uncertainty quantification. The object-oriented nature of the code allows for easily interchanging different solution methods and different physics problems. It provides a simple interface for the users to supply their domain-specific physics models. Finally, the code can be used as a test-bed for new ensemble-based data assimilation and field inversion methods.DL-PDE: deep-learning based data-driven discovery of partial differential equations from discrete and noisy datahttps://zbmath.org/1528.650932024-03-13T18:33:02.981707Z"Xu, Hao"https://zbmath.org/authors/?q=ai:xu.hao.5"Chang, Haibin"https://zbmath.org/authors/?q=ai:chang.haibin"Zhang, Dongxiao"https://zbmath.org/authors/?q=ai:zhang.dongxiaoSummary: In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is to discover unknown physics and corresponding equations. However, prior to achieving this goal, major challenges remain to be resolved, including learning PDE under noisy data and limited discrete data. To overcome these challenges, in this work, a deep-learning based data-driven method, called DL-PDE, is developed to discover the governing PDEs of underlying physical processes. The DL-PDE method combines deep learning via neural networks and data-driven discovery of PDE via sparse regressions. In the DL-PDE, a neural network is first trained, then a large amount of meta-data is generated, and the required derivatives are calculated by automatic differentiation. Finally, the form of PDE is discovered by sparse regression. The proposed method is tested with physical processes, governed by the diffusion equation, the convection-diffusion equation, the Burgers equation, and the Korteweg-de Vries (KdV) equation, for proof-of-concept and applications in real-world engineering settings. The proposed method achieves satisfactory results when data are noisy and limited.Information-theoretic interpretation of quantum formalismhttps://zbmath.org/1528.810082024-03-13T18:33:02.981707Z"Feldmann, Michel"https://zbmath.org/authors/?q=ai:feldmann.michel.1Summary: We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to classical constraints, based on a question-and-answer procedure. The problem is posed from a particular batch of queries while the constraints are represented by the truth table of a set of Boolean functions. The Bayesian inference technique consists in assigning a probability distribution within a real-valued probability space to the joint set of queries in order to satisfy the constraints. The initial query batch is not unique and alternative batches can be considered at will. They are enabled mechanically from the initial batch, quite simply by transcribing the probability space into an auxiliary Hilbert space. It turns out that this sole procedure leads to exactly rediscover the standard quantum information theory and thus provides an information-theoretic rationale to its technical rules. In this framework, the great challenges of quantum mechanics become simple platitudes: Why is the theory probabilistic? Why is the theory linear? Where does the Hilbert space come from? In addition, most of the paradoxes, such as uncertainty principle, entanglement, contextuality, nonsignaling correlation, measurement problem, etc., become straightforward features. In the end, our major conclusion is that quantum information is nothing but classical information processed by a mature form of Bayesian inference technique and, as such, consubstantial with Aristotelian logic.Data-driven and almost model-independent reconstruction of modified gravityhttps://zbmath.org/1528.830542024-03-13T18:33:02.981707Z"Mu, Yuhao"https://zbmath.org/authors/?q=ai:mu.yuhao"Li, En-Kun"https://zbmath.org/authors/?q=ai:li.en-kun"Xu, Lixin"https://zbmath.org/authors/?q=ai:xu.lixin.1(no abstract)Coupling quintessence kinetics to electromagnetismhttps://zbmath.org/1528.831252024-03-13T18:33:02.981707Z"Barros, Bruno J."https://zbmath.org/authors/?q=ai:barros.bruno-jose-s"da Fonseca, Vitor"https://zbmath.org/authors/?q=ai:da-fonseca.vitor(no abstract)Bayesian inference on the Allee effect in cancer cell line populations using time-lapse microscopy imageshttps://zbmath.org/1528.920152024-03-13T18:33:02.981707Z"Lindwall, Gustav"https://zbmath.org/authors/?q=ai:lindwall.gustav"Gerlee, Philip"https://zbmath.org/authors/?q=ai:gerlee.philipSummary: The Allee effect describes the phenomenon that the per capita reproduction rate increases along with the population density at low densities. Allee effects have been observed at all scales, including in microscopic environments where individual cells are taken into account. This is great interest to cancer research, as understanding critical tumour density thresholds can inform treatment plans for patients. In this paper, we introduce a simple model for cell division in the case where the cancer cell population is modelled as an interacting particle system. The rate of the cell division is dependent on the local cell density, introducing an Allee effect. We perform parameter inference of the key model parameters through Markov chain Monte Carlo, and apply our procedure to two image sequences from a cervical cancer cell line. The inference method is verified on \textit{in silico} data to accurately identify the key parameters, and results on the \textit{in vitro} data strongly suggest an Allee effect.