Abstract
An important issue for robust inference is to examine the stability of the asymptotic level and power of the test statistic in the presence of contaminated data. Most existing results are derived in finite-dimensional settings with some particular choices of loss functions. This paper re-examines this issue by allowing for a diverging number of parameters combined with a broader array of robust error measures, called “robust-”, for the class of “general linear models”. Under regularity conditions, we derive the influence function of the robust- parameter estimator and demonstrate that the robust- Wald-type test enjoys the robustness of validity and efficiency asymptotically. Specifically, the asymptotic level of the test is stable under a small amount of contamination of the null hypothesis, whereas the asymptotic power is large enough under a contaminated distribution in a neighborhood of the contiguous alternatives, thus lending supports to the utility of the proposed robust- Wald-type test.
Highlights
The class of varying-dimensional “general linear models” [1], including the conventional generalized linear model (GLM in [2]), is flexible and powerful for modeling a large variety of data and plays an important role in many statistical applications
The study of robust testing includes two aspects: (i) establishing the stability of the asymptotic level under small departures from the null hypothesis; and (ii) demonstrating that the asymptotic power is sufficiently large under small departures from specified alternatives
Heritier et al [10] studied the robustness properties of the Wald, score and likelihood ratio tests based on M estimators for general parametric models
Summary
The class of varying-dimensional “general linear models” [1], including the conventional generalized linear model (GLM in [2]), is flexible and powerful for modeling a large variety of data and plays an important role in many statistical applications. Heritier et al [10] studied the robustness properties of the Wald, score and likelihood ratio tests based on M estimators for general parametric models. It remains an important issue to examine the robustness property of the robust-BD Wald-type test [1] in the varying-dimensional case, i.e., whether the test still has stable asymptotic level and power, in the presence of contaminated data. Wald-type tests have been established for the M estimators [10], generalized method of moment estimators [13], minimum density power divergence estimator [17] and general M estimators under random censoring [18], their results for finite-dimensional settings are not directly applicable to our situations with a diverging number of parameters.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
