Robust Bounded Influence Tests in Linear Models
Abstract
A robust test, which we call an aligned generalized, M-test for testing subhypotheses in the general linear models is developed, and its asymptotic properties are studied. The test is a robustification of the well known F-test, and it is an elegant and practical alternative to Ronchetti's (1982) class of tau-tests. P-values associated with it can be approximated readily using existing chi square tables, unlike Ronchetti's test. The test is based on an appropriately constructed quadratic form, and uses the generalized M-estimators of the parameters in the reduced model. Under the null hypothesis the asymptotic distribution is a central chi square, and under contiguous alternatives is a non-central chi square with the same degrees of freedom. The test can also be viewed as a generalization of Sen's (1982) M-test for linear models. The influence function of the test is bounded. The bound not only applies to the influence of residuals but also to the influence of position in the factor space. Sen's test, on the other hand, has bounded influence only in residuals.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1988
- Accession Number
- ADA201896
Entities
People
- Marianthi Markatou
- Thomas P. Hettmansperger
Organizations
- Pennsylvania State University