Robust Wald-type tests based on minimum Rényi pseudodistance estimators for the multiple linear regression model

Abstract

We introduce a new family of Wald-type tests, based on minimum Rényi pseudodistance estimators, for testing general linear hypotheses and the variance of the residuals in the multiple regression model. The classical Wald test, based on the maximum likelihood estimator, can be seen as a particular case inside our family. Theoretical results, supported by an extensive simulation study, point out how some tests included in this family have a better behaviour, in the sense of robustness, than the Wald test. Finally, we provide a data-driven procedure for the choice of the optimal test given any data set.

Keywords:

• Influence function
• minimum density power divergence estimator
• multiple regression model
• Rényi pseudodistance
• robustness

2010 Mathematics Subject Classifications:

• 62J05
• 62F12
• 62F35
• 62H15
• 62F10

Acknowledgements

The authors would like to thank the reviewer for his/her helpful comments and suggestions. This research is partially supported by Grant PGC2018-005194-B-100 and Grant FPU16/0314 from Ministerio de Ciencia, Innovación y Universidades (Spain). E. Castilla, N. Martín and L. Pardo are members of the Instituto de Matemática Interdisciplinar, Complutense University of Madrid.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is partially supported by Grant PGC2018-005194-B-100 and Grant FPU16/03104 from Ministerio de Ciencia, Innovación y Universidades (Spain). E. Castilla, N. Martín and L. Pardo are members of the Instituto de Matemática Interdisciplinar, Complutense University of Madrid.