Testing Composite Hypothesis based on the Density Power Divergence

Abstract

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. (1998) provides a flexible class of divergences where the adjustment between efficiency and robustness is controlled by a single parameter $\beta$. 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.

34 pages, 6 figures

References in corpus (5)

• Generalized Wald-type Tests based on Minimum Density Power Divergence Estimators
• Several Applications of Divergence Criteria in Continuous Families
• On the Robustness of a Divergence based Test of Simple Statistical Hypotheses
• Robust Tests for the Equality of Two Normal Means based on the Density Power Divergence
• Testing Composite Null Hypothesis Based on $S$-Divergences

Cited by in corpus (5)

• Generalized Wald-type Tests based on Minimum Density Power Divergence Estimators
• On the Robustness of a Divergence based Test of Simple Statistical Hypotheses
• The Minimum S-Divergence Estimator under Continuous Models: The Basu-Lindsay Approach
• Testing Composite Null Hypothesis Based on $S$-Divergences
• On minimum Bregman divergence inference