×

Semiparametric inference on general functionals of two semicontinuous populations. (English) Zbl 07523345

Summary: In this paper, we propose new semiparametric procedures for inference on linear functionals in the context of two semicontinuous populations. The distribution of each semicontinuous population is characterized by a mixture of a discrete point mass at zero and a continuous skewed positive component. To utilize the information from both populations, we model the positive components of the two mixture distributions via a semiparametric density ratio model. Under this model setup, we construct the maximum empirical likelihood estimators of the linear functionals. The asymptotic normality of the proposed estimators is established and is used to construct confidence regions and perform hypothesis tests for these functionals. We show that the proposed estimators are more efficient than the fully nonparametric ones. Simulation studies demonstrate the advantages of our method over existing methods. Two real-data examples are provided for illustration.

MSC:

62-XX Statistics

Software:

bootstrap
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Anderson, JA, Multivariate logistic compounds, Biometrika, 66, 17-26 (1979) · Zbl 0399.62029 · doi:10.1093/biomet/66.1.17
[2] Böhning, D.; Alfò, M., Editorial: Special issue on models for continuous data with a spike at zero, Biometrical Journal, 58, 255-258 (2016) · doi:10.1002/bimj.201500188
[3] Brunner, E.; Dette, H.; Munk, A., Box-type approximations in nonparametric factorial designs, Journal of the American Statistical Association, 92, 1494-1502 (1997) · Zbl 0921.62096 · doi:10.1080/01621459.1997.10473671
[4] Cai, S.; Chen, J., Empirical likelihood inference for multiple censored samples, The Canadian Journal of Statistics, 46, 2, 212-232 (2018) · Zbl 1474.62344 · doi:10.1002/cjs.11348
[5] Cai, S.; Chen, J.; Zidek, JV, Hypothesis test in the presence of multiple samples under density ratio models, Statistica Sinica, 27, 761-783 (2017) · Zbl 1368.62111
[6] Chen, J.; Liu, Y., Quantile and quantile-function estimations under density ratio model, The Annals of Statistics, 41, 1669-1692 (2013) · Zbl 1292.62072
[7] Chen, Y.-H., Zhou, X.-H. (2006). Generalized confidence intervals for the ratio or difference of two means for lognormal populations with zeros. Working Paper 296, UW Biostatistics Working Paper Series. https://biostats.bepress.com/uwbiostat/paper296.
[8] Dufour, J-M; Flachaire, E.; Khalaf, L., Permutation tests for comparing inequality measures, Journal of Business and Economic Statistics, 37, 457-470 (2019) · doi:10.1080/07350015.2017.1371027
[9] Efron, B.; Tibshirani, RJ, An introduction to the bootstrap (1993), New York: Chapman and Hall, New York · Zbl 0835.62038 · doi:10.1007/978-1-4899-4541-9
[10] Fernholz, LT, von Mises calculus for statistical functionals (1983), New York: Springer, New York · Zbl 0525.62031 · doi:10.1007/978-1-4612-5604-5
[11] Jiang, S.; Tu, D., Inference on the probability \(P(T_1<T_2)\) as a measurement of treatment effect under a density ratio model and random censoring, Computational Statistics and Data Analysis, 56, 1069-1078 (2012) · doi:10.1016/j.csda.2011.02.011
[12] Kang, L.; Vexler, A.; Tian, L.; Cooney, M.; Louis, GMB, Empirical and parametric likelihood interval estimation for populations with many zero values: Application for assessing environmental chemical concentrations and reproductive health, Epidemiology, 21, S58-S63 (2010) · doi:10.1097/EDE.0b013e3181d7eb68
[13] Kay, R.; Little, S., Transformations of the explanatory variables in the logistic regression model for binary data, Biometrika, 74, 495-501 (1987) · Zbl 0635.62075 · doi:10.1093/biomet/74.3.495
[14] Koopmans, LH, Introduction to contemporary statistical methods (1981), Boston: Duxbury Press, Boston · Zbl 0549.62001
[15] Li, H.; Liu, Y.; Liu, Y.; Zhang, R., Comparison of empirical likelihood and its dual likelihood under density ratio model, Journal of Nonparametric Statistics, 30, 581-597 (2018) · Zbl 1403.62048 · doi:10.1080/10485252.2018.1457790
[16] Lu, Y-H; Liu, A-Y; Jiang, M-J; Jiang, T., A new two-part test based on density ratio model for zero-inflated continuous distributions, Applied Mathematics-A Journal of Chinese Universities, 35, 203-219 (2020) · Zbl 1463.62037 · doi:10.1007/s11766-020-3957-x
[17] Neuhauser, M., Nonparametric statistical tests: A computational approach (2011), Boca Raton: CRC Press, Boca Raton · doi:10.1201/b11427
[18] Nixon, RM; Thompson, SG, Parametric modelling of cost data in medical studies, Statistics in Medicine, 23, 1311-1331 (2004) · doi:10.1002/sim.1744
[19] Owen, A., Empirical likelihood (2001), New York: CRC Press, New York · Zbl 0989.62019 · doi:10.1201/9781420036152
[20] Pauly, M.; Brunner, E.; Konietschke, F., Asymptotic permutation tests in general factorial designs, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 77, 461-473 (2015) · Zbl 1414.62339 · doi:10.1111/rssb.12073
[21] Qin, J., Biased sampling, over-identified parameter problems and beyond (2017), Singapore: Springer, Singapore · Zbl 1441.62008 · doi:10.1007/978-981-10-4856-2
[22] Qin, J.; Zhang, B., A goodness-of-fit test for logistic regression models based on case-control data, Biometrika, 84, 609-618 (1997) · Zbl 0888.62045 · doi:10.1093/biomet/84.3.609
[23] Satter, F.; Zhao, Y., Jackknife empirical likelihood for the mean difference of two zero-inflated skewed populations, Journal of Statistical Planning and Inference, 211, 414-422 (2021) · Zbl 1455.62096 · doi:10.1016/j.jspi.2020.07.009
[24] Serfling, RJ, Approximation theorems of mathematical statistics (1980), New York: Wiley, New York · Zbl 0538.62002 · doi:10.1002/9780470316481
[25] Shao, J.; Tu, D., The jackknife and bootstrap (1995), New York: Springer, New York · Zbl 0947.62501 · doi:10.1007/978-1-4612-0795-5
[26] Tu, W.; Zhou, X-H, A Wald test comparing medical costs based on log-normal distributions with zero valued costs, Statistics in Medicine, 18, 2749-2761 (1999) · doi:10.1002/(SICI)1097-0258(19991030)18:20<2749::AID-SIM195>3.0.CO;2-C
[27] Wang, C.; Marriott, P.; Li, P., Testing homogeneity for multiple nonnegative distributions with excess zero observations, Computational Statistics and Data Analysis, 114, 146-157 (2017) · Zbl 1464.62177 · doi:10.1016/j.csda.2017.04.011
[28] Wang, C.; Marriott, P.; Li, P., Semiparametric inference on the means of multiple nonnegative distributions with excess zero observations, Journal of Multivariate Analysis, 166, 182-197 (2018) · Zbl 1499.62184 · doi:10.1016/j.jmva.2018.02.010
[29] Wu, C.; Yan, Y., Empirical likelihood inference for two-sample problems, Statistics and Its Interface, 5, 345-354 (2012) · Zbl 1383.62137 · doi:10.4310/SII.2012.v5.n3.a7
[30] Yuan, M.; Li, P.; Wu, C., Semiparametric inference of the Youden index and the optimal cut-off point under density ratio models, The Canadian Journal of Statistics (2021) · Zbl 1492.62070 · doi:10.1002/cjs.11600
[31] Zhou, X-H; Tu, W., Comparison of several independent population means when their samples contain log-normal and possibly zero observations, Biometrics, 55, 645-651 (1999) · Zbl 1059.62518 · doi:10.1111/j.0006-341X.1999.00645.x
[32] Zhou, X-H; Tu, W., Interval estimation for the ratio in means of log-normally distributed medical costs with zero values, Computational Statistics and Data Analysis, 35, 201-210 (2000) · Zbl 1115.62302 · doi:10.1016/S0167-9473(00)00009-8
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.