Empirical phi-divergence test statistics for testing simple and composite null hypotheses

References

• Owen AB. Empirical likelihood ratio confidence interval for a single functional. Biometrika. 1988;75:308–313. doi: 10.1093/biomet/75.2.237
   Web of Science ®Google Scholar
• Qin J, Lawless J. Empirical likelihood and general estimating equations. Ann Statist. 1994;22:300–325. doi: 10.1214/aos/1176325370
   Web of Science ®Google Scholar
• Owen AB. Empirical likelihood confidence regions. Ann Statist. 1990;18:90–120. doi: 10.1214/aos/1176347494
   Web of Science ®Google Scholar
• Broniatowski M, Keziou A. Divergences and duality for estimating and test under moment condition models. J Statist Plann Inference. 2012;142:2554–2573. doi: 10.1016/j.jspi.2012.03.013
   Web of Science ®Google Scholar
• Baggerly KA. Empirical likelihood as a goodness-of-fit measure. Biometrika. 1998;85:535–547. doi: 10.1093/biomet/85.3.535
   Web of Science ®Google Scholar
• Pardo L. Statistical inference based on divergence measures. Boca Raton, FL: Chapman & Hall/ CRC Press; 2006.
   Google Scholar
• Basu A, Shioya H, Park C. Statistical inference: the minimum distance approach. Boca Raton, FL: Chapman & Hall/CRC Press; 2011.
   Google Scholar
• van der Vaart AW. Asymptotic statistics. Cambridge: Cambridge University Press; 2000.
   Google Scholar
• Schennach SM. Point estimation with exponentially tilted empirical likelihood. Ann Statist. 2007;35:634–672. doi: 10.1214/009053606000001208
   Web of Science ®Google Scholar
• Ragusa G. Minimum divergence, generalized empirical likelihoods, and higher order expansions. Econom Rev. 2011;30(4):406–456. doi: 10.1080/07474938.2011.553541
   Web of Science ®Google Scholar
• Toma A. Robustness of dual divergence estimators for models satisfying linear constraints. C. R. Acad. Sci. Paris, Ser. I. 2013;351:311–316. doi: 10.1016/j.crma.2013.02.005
   Web of Science ®Google Scholar
• Bhattacharyya A. On a measure of divergence between two statistical populations defined by their probability distributions. Bull Calcutta Math Soc. 1943;35:99–109.
   Google Scholar
• Rényi A. On measures of entropy and information. Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, vol. 1; 1961. p. 547–561.
   Google Scholar
• Sharma BD, Mittal DP. New non-additive measures of relative information. Comb Inf Syst Sci. 1997;2:122–133.
   Google Scholar
• Menéndez ML, Morales D, Pardo L, Salicrú M. Asymptotic behavior and statistical applications of divergence measures in multinomial populations: a unified study. Statist Papers. 1995;36:1–29. doi: 10.1007/BF02926015
   Web of Science ®Google Scholar
• Menéndez ML, Pardo JA, Pardo L, Pardo MC. Asymptotic approximations for the distributions of the (h, φ)-divergence goodness-of-fit statistics: applications to Rényi ’s statistic. Kybernetes. 1997;26:442–452. doi: 10.1108/03684929710176449
   Web of Science ®Google Scholar
• Heritier S, Ronchetti E. Robust bounded-influence tests in general parametric models. J Am Statist Assoc. 1994;89:897–904. doi: 10.1080/01621459.1994.10476822
   Web of Science ®Google Scholar
• Toma A. Optimal robust M-estimators using divergences. Statist Probab Lett. 2009;79:1–5. doi: 10.1016/j.spl.2008.04.011
   Web of Science ®Google Scholar
• Fraser DAS. Nonparametric methods in statistics. New York, NY: John Wiley & Sons; 1957.
   Google Scholar
• Le Cam L. Locally asymptotic normal families of distributions. Berkeley, CA: University of California Press; 1960.
   Google Scholar
• Hájek J, Sidák Z. Theory of rank tests. New York, NY: Academic Press; 1967.
   Google Scholar
• Morales D, Pardo L. Some approximations to power functions of φ-divergence tests in parametric models. TEST. 2001;10:249–269.
   Google Scholar
• Stigler SM. Simon Newcomb, Percy Daniell, and the history of robust estimation, 1885–1920. J Amer Statist Assoc. 1973;68:872–879.
   Web of Science ®Google Scholar
• Voinov V, Nikulin MS, Balakrishnan N. Chi-squared goodness of fit tests with applications. Boston: Academic Press; 2013.
   Google Scholar
• Barnett V, Lewis T. Outliers in statistical data. 3rd ed. Chichester, England: John Wiley & Sons; 1994.
   Google Scholar
• Cressie N, Read TRC. Multinomial goodness-of-fit tests. J R Statist Soc, Ser B. 1984;46:440–464.
   Google Scholar
• Gokhale DV, Kullback S. The information in contingency tables. New York, NY: Marcel Dekker; 1978.
   Google Scholar