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Testing Composite Hypothesis Based on the Density Power Divergence

A. Basu (), A. Mandal, N. Martin and L. Pardo
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A. Basu: Indian Statistical Institute
A. Mandal: Wayne State University
N. Martin: Complutense University of Madrid
L. Pardo: Complutense University of Madrid

Sankhya B: The Indian Journal of Statistics, 2018, vol. 80, issue 2, 222-262

Abstract: 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. (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.

Keywords: Density power divergence; linear combination of chi-squares; robustness; tests of hypotheses.; Primary 62F03; Secondary 62F35 (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:spr:sankhb:v:80:y:2018:i:2:d:10.1007_s13571-017-0143-0