Generalized Wald-type tests based on minimum density power divergence estimators

Abstract

In testing of hypothesis, the robustness of the tests is an important concern. Generally, the maximum likelihood-based tests are most efficient under standard regularity conditions, but they are highly non-robust even under small deviations from the assumed conditions. In this paper, we have proposed generalized Wald-type tests based on minimum density power divergence estimators for parametric hypotheses. This method avoids the use of nonparametric density estimation and the bandwidth selection. The trade-off between efficiency and robustness is controlled by a tuning parameter β. The asymptotic distributions of the test statistics are chi-square with appropriate degrees of freedom. The performance of the proposed tests is explored through simulations and real data analysis.

Keywords:

• density power divergence
• robustness
• tests of hypotheses

AMS 2010 Subject Classification:

• Primary: 62F35
• Secondary: 62F03

Acknowledgements

The authors gratefully acknowledge the suggestions of the editor, the associate editor and two anonymous referees which led to an improved version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was partially supported by Grant [MTM-2012-33740] and [ECO-2011-25706].