Robust tests for linear regression models based on τ-estimates

Abstract

ANOVA tests are the standard tests to compare nested linear models fitted by least squares. These tests are equivalent to likelihood ratio tests, so they have high power. However, least squares estimators are very vulnerable to outliers in the data, and thus the related ANOVA type tests are also extremely sensitive to outliers. Therefore, robust estimators can be considered to obtain a robust alternative to the ANOVA tests. Regression τ-estimators combine high robustness with high efficiency which makes them suitable for robust inference beyond parameter estimation. Robust likelihood ratio type test statistics based on the τ-estimates of the error scale in the linear model are a natural alternative to the classical ANOVA tests. The higher efficiency of the τ-scale estimates compared with other robust alternatives is expected to yield tests with good power. Their null distribution can be estimated using either an asymptotic approximation or the fast and robust bootstrap. The robustness and power of the resulting robust likelihood ratio type tests for nested linear models is studied.