Testing Composite Hypothesis Based on the Density Power Divergence
In any parametric inference problem, the robustness of the procedure is a real concern. A procedure which retains a high degree of efficiency under the model and simultaneously provides stable inference under data contamination is preferable in any practical situation over another procedure which achieves its efficiency at the cost of robustness or vice versa. The density power divergence family of Basu et al. (Biometrika 85, 549–559 1998) provides a flexible class of divergences where the adjustment between efficiency and robustness is controlled by a single parameter β. In this paper we consider general tests of parametric hypotheses based on the density power divergence. We establish the asymptotic null distribution of the test statistic and explore its asymptotic power function. Numerical results illustrate the performance of the theory developed.
KeywordsDensity power divergence linear combination of chi-squares robustness tests of hypotheses.
Subject ClassificationPrimary 62F03 Secondary 62F35
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This work was partially supported by Grant MTM-2015-67057-P. The authors gratefully acknowledge the suggestions of two anonymous referees which led to an improved version of the paper. The authors would like to thank Dr. Abhik Ghosh for preparing the plot of the influence function.
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