Model Selection in a Composite Likelihood Framework Based on Density Power Divergence

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This paper presents a model selection criterion in a composite likelihood framework based on density power divergence measures and in the composite minimum density power divergence estimators, which depends on an tuning parameter α. After introducing such a criterion, some asymptotic properties are established. We present a simulation study and two numerical examples in order to point out the robustness properties of the introduced model selection criterion.
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1. Fearnhead, P.; Donnelly, P. Approximate likelihood methods for estimating local recombination rates. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 2002, 64, 657–680. 2. Renard, ; D.; Molenberghs, G.; Geys, H. A pairwise likelihood approach to estimation in multilevel probit models. J. Comput. Stat. Data Anal. 2004, 44, 649–667. 3. Hjort, N.L.; Omre, H. Topics in spatial statistics. Scand. J. Stat. 1994, 21, 289–357. 4. Heagerty, P.J.; Lele, S.R. A composite likelihood approach to binary spatial data. J. Am. Stat. Assoc. 1998, 93, 1099–1111. 5. Varin, C.; Host, G.; Skare, O. Pairwise likelihood inference in spatial generalized linear mixed models. Comput. Stat. Data Anal. 2005, 49, 1173–1191 6. Henderson, R.; Shimakura, S. A serially correlated gamma frailty model for longitudinal count data. Biometrika 2003, 90, 355–366. 7. Parner, E.T. A composite likelihood approach to multivariate survival data. Scand. J. Stat. 2001, 28, 295–302. 8. Li, Y.; Lin, X. Semiparametric Normal Transformation Models for Spatially Correlated Survival Data. J. Am. Stat. Assoc. 2006, 101, 593–603. 9. Joe, H.; Reid, N.; Somg, P.X.; Firth, D.; Varin, C. Composite Likelihood Methods. Report on the Workshop on Composite Likelihood. 2012. Available online: (accessed on 23 July 2019). 10. Varin, C.; Reid, N.; Firth, D. An overview of composite likelihood methods. Statist. Sin. 2011, 21, 5–42. 11. Martín, N.; Pardo, L.; Zografos, K. On divergence tests for composite hypotheses under composite likelihood. Stat. Pap. 2019, 60, 1883–1919. 12. Castilla, E.; Martin, N.; Pardo, L.; Zografos, K. Composite Likelihood Methods Based on Minimum Density Power Divergence Estimator. Entropy 2018, 20, 18. 13. Castilla, E.; Martin, N.; Pardo, L.; Zografos, K. Composite likelihood methods: Rao-type tests based on composite minimum density power divergence estimator. Stat. Pap. 2019. 14. Kullback, S. Information Theory and Statistics; Wiley: New York, NY, USA, 1959. 15. Akaike, H. Information theory and an extension of the maximum likelihood principle. In 2nd International Symposium on Information Theory; Petrov, B.N., Csaki, F., Eds.; Akademiai Kiado: Budapest, Hungary, 1973; pp. 267–281 . 16. Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control 1974, 19, 716–723. 17. Takeuchi, K. Distribution of information statistics and criteria for adequacy of models. Math. Sci. 1976, 153, 12–18. (In Japanese) 18. Murari, A.; Peluso, E.; Cianfrani, F.; Gaudio, P.; Lungaroni, M. On the Use of Entropy to Improve Model Selection Criteria. Entropy 2019, 21, 394. 19. Mattheou, K.; Lee, S.; Karagrigoriou, A. A model selection criterion based on the BHHJ measure of divergence. J. Stat. Plan. Inference 2009, 139, 228–235. 20. Avlogiaris, G.; Micheas, A.; Zografos, K. A criterion for local model selection. Shankhya 2019, 81, 406–444. 21. Avlogiaris, G.; Micheas, A.; Zografos, K. On local divergences between two probability measures. Metrika 2016, 79, 303–333. 22. Varin, C.; Vidoni, P. A note on composite likelihood inference and model selection. Biometrika 2005, 92, 519–528. 23. Gao, X.; Song, P.X.K. Composite likelihood Bayesian information criteria for model selection in high-dimensional data. J. Am. Stat. Assoc. 2010, 105, 1531–1540. 24. Ng, C.T.; Joe, H. Model comparison with composite likelihood information criteria. Bernoulli 2014, 20, 1738–1764. 25. Basu, A.; Harris, I.R.; Hjort, N.L.; Jones, M.C. Robust and efficient estimation by minimizing a density power divergence. Biometrika 1998, 85, 549–559. 26. Pardo, L. Statistical Inference Based on Divergence Measures; Chapman & Hall CRC Press: Boca Raton, FL, USA, 2006. 27. Basu, A.; Shioya, H.; Park, C. Statistical Inference. The Minimum Distance Approach; Chapman & Hall/CRC: Boca Raton, FL, USA, 2011. 28. Burham, K.P.; Anderson, D.R. Model Selection and Multinomial Inference: A Practical Information-Theoretic Approach; Springer: New York, NY, USA, 2002. 29. Xu, X., Reid, N. On the robustness of maximum composite estimate. J. Stat. Plan. Inference 2011, 141, 3047–3054. 30. Warwick, J.; Jones, M.C. Choosing a robustness tuning parameter. J. Stat. Comput. Simul. 2005, 75, 581–588. 31. Fisher, R.A. The use of multiple measurements in taxonomic problems. Ann. Eugenics. 1936, 7, 179–188. 32. Fraley, A.; Raftery, E.; Murphy, T.B.; Scrucca, L. MCLUST Version 4 for R: Normal Mixture Modeling for Model-based Clustering, Classification, and Density Estimation; Technical Report 597; Department of Statistics, University of Washington: Seattle, WA, USA, 2012. 33. Forina, M.; Lanteri, S.; Armanino, C.; Leardi, R. PARVUS: An Extendable Package of Programs for Data Exploration, Classification, and Correlation; Institute of Pharmaceutical and Food Analysis Technologies: Genoa, Italy, 1998.