A Robust Generalization of the Rao Test

Abstract

This article presents new families of Rao-type test statistics based on the minimum density power divergence estimators which provide robust generalizations for testing simple and composite null hypotheses. The asymptotic null distributions of the proposed tests are obtained and their robustness properties are also theoretically studied. Numerical illustrations are provided to substantiate the theory developed. On the whole, the proposed tests are seen to be excellent alternatives to the classical Rao test as well as other well-known tests.

KEYWORDS:

• Influence function
• Minimum density power divergence estimator
• Power and level influence function
• Rao test
• Rao-type test

Supplementary Materials

The supplemental material includes an appendix with 1. Basu et al. regularity conditions (Basu et al. 2011); 2. Equivalence of the maximum Lq-likelihood and minimum DPD estimators; 3. Additional details for examples; 4. Additional details and scenario for simulation study; 5. Proofs of main results.

Acknowledgments

We thank the editor and the three referees for their constructive and helpful suggestions.

Additional information

Funding

This work was partially supported by research grants, numbered CRG/2019/001461 from the Science and Engineering Research Board, Government of India (A. Ghosh) and, numbered PGC2018-095194-B-I00 from Ministerio de Ciencia, Innovación y Universidades, Government of Spain (N. Martín and L. Pardo).