De Bin, Riccardo; Sartori, Nicola; Severini, Thomas A. Integrated likelihoods in models with stratum nuisance parameters. (English) Zbl 1327.62304 Electron. J. Stat. 9, No. 1, 1474-1491 (2015). Summary: Frequentist inference about a parameter of interest in presence of a nuisance parameter can be based on an integrated likelihood function. We analyze the behaviour of inferential quantities based on such a pseudo-likelihood in a two-index-asymptotics framework, in which both sample size and dimension of the nuisance parameter may diverge to infinity. We show that a properly chosen integrated likelihood largely outperforms standard likelihood methods, such as those based on the profile likelihood. These results are confirmed by simulation studies, in which comparisons with modified profile likelihood are also considered. Cited in 8 Documents MSC: 62G20 Asymptotic properties of nonparametric inference Keywords:modified profile likelihood; non stationary autoregressive model; profile likelihood; profile score bias; two-index asymptotics Software:QUADPACK × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] Abramowitz, M. and Stegun, I. A. (1964)., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables . Dover Publications, New York. · Zbl 0171.38503 [2] Arellano, M. and Bonhomme, S. (2009). Robust priors in nonlinear panel data models., Econometrica 77 489-536. · Zbl 1161.62078 · doi:10.3982/ECTA6895 [3] Barndorff-Nielsen, O. E. (1996). Two order asymptotic. In, Frontiers in Pure and Applied Probability II: Proceedings of the Fourth Russian-Finnish Symposium Prob. Th. Math. Statist. (A. Melnikov, ed.) 9-20. TVP Science, Moscow. · Zbl 0899.62044 [4] Barndorff-Nielsen, O. E. and Cox, D. R. (1994)., Inference and Asymptotics . Chapman and Hall, London. · Zbl 0826.62004 [5] Bartolucci, F., Bellio, R., Salvan, A. and Sartori, N. (2015). Modified profile likelihood for fixed effects panel data models., Econometric Reviews , [6] Bellio, R. and Guolo, A. (2015). Integrated likelihood inference in small sample meta-analysis for continuous outcomes., Scandinavian Journal of Statistics , · Zbl 1371.62058 [7] Berger, J. O., Liseo, B. and Wolpert, R. L. (1999). Integrated likelihood methods for eliminating nuisance parameters., Statistical Science 14 1-22. · Zbl 1059.62521 · doi:10.1214/ss/1009211804 [8] Cox, D. R. and Reid, N. (1987). Parameter orthogonality and approximate conditional inference., Journal of the Royal Statistical Society. Series B (Methodological) 49 1-39. · Zbl 0616.62006 [9] Cox, D. R. and Reid, N. (1993). A note on the calculation of adjusted profile likelihood., Journal of the Royal Statistical Society. Series B (Methodological) 55 467-471. · Zbl 0797.62015 [10] Davison, A. C. (1988). Approximate conditional inference in generalized linear models., Journal of the Royal Statistical Society. Series B (Methodological) 50 445-461. [11] Dhaene, G. and Jochmans, K. (2014). Likelihood inference in an autoregression with fixed effects., Econometric Theory FirstView 1-38. · Zbl 1441.62668 [12] Efron, B. (1993). Bayes and likelihood calculations from confidence intervals., Biometrika 80 3-26. · Zbl 0773.62021 · doi:10.1093/biomet/80.1.3 [13] Evans, M. and Swartz, T. (2000)., Approximating Integrals via Monte Carlo and Deterministic Methods . Oxford University Press, New York. · Zbl 0958.65009 [14] Kalbfleisch, J. D. and Sprott, D. A. (1970). Application of likelihood methods to models involving large numbers of parameters., Journal of the Royal Statistical Society. Series B (Methodological) 32 175-208. · Zbl 0205.45903 [15] Lancaster, T. (2002). Orthogonal parameters and panel data., Review of Economic Studies 69 647-666. · Zbl 1008.62115 · doi:10.1111/1467-937X.t01-1-00025 [16] Pace, L. and Salvan, A. (1997)., Principles of Statistical Inference: From a Neo-Fisherian Perspective . World Scientific, Singapore. · Zbl 0911.62003 [17] Piessens, R., de Doncker-Kapenga, E., Überhuber, C. and Kahaner, D. (1983)., Quadpack: A Subroutine Package for Automatic Integration . Springer Verlag, Berlin. · Zbl 0508.65005 [18] Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P. (2007)., Numerical Recipes: The Art of Scientific Computing . Cambridge University Press, New York. · Zbl 1132.65001 [19] Reid, N. (2003). Asymptotics and the theory of inference., Annals of Statistics 21 1695-1731. · Zbl 1042.62022 · doi:10.1214/aos/1074290325 [20] Sartori, N. (2003). Modified profile likelihoods in models with stratum nuisance parameters., Biometrika 90 533-549. · Zbl 1436.62086 · doi:10.1093/biomet/90.3.533 [21] Severini, T. A. (1998). An approximation to the modified profile likelihood function., Biometrika 85 403-411. · Zbl 1048.62504 · doi:10.1093/biomet/85.2.403 [22] Severini, T. A. (2000)., Likelihood Methods in Statistics . Oxford University Press, New York. · Zbl 0984.62002 [23] Severini, T. A. (2007). Integrated likelihood functions for non-Bayesian inference., Biometrika 94 529-542. · Zbl 0958.65009 · doi:10.1093/biomet/asm040 [24] Severini, T. A. (2010). Likelihood ratio statistics based on an integrated likelihood., Biometrika 97 481-496. · Zbl 1406.62023 · doi:10.1093/biomet/asq015 [25] Severini, T. A. (2011). Frequency properties of inferences based on an integrated likelihood function., Statistica Sinica 21 433-447. · Zbl 1206.62033 [26] Sweeting, T. J. (1987). Discussion of the paper by Cox and Reid., Journal of the Royal Statistical Society. Series B (Methodological) 49 20-21. [27] Ventura, L., Cabras, S. and Racugno, W. (2009). Prior distributions from pseudo-likelihoods in the presence of nuisance parameters., Journal of the American Statistical Association 104 768-774. · Zbl 1388.62060 · doi:10.1198/jasa.2009.0133 [28] Wooldridge, J. M. (1994). Estimation and inference for dependent processes., Handbook of Econometrics 4 2639-2738. · doi:10.1016/S1573-4412(05)80014-5 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.