Bounded Influence and High Breakdown Point Testing Procedures in Linear Models

Abstract

Three classes of testing procedures based on one-step high breakdown point bounded influence estimators, for testing subhypotheses in linear models are developed. These are drop-in-dispersion, Wald-type, and score-type tests. The asymptotic distributions of these testing procedures are obtained under the null hypothesis and under contiguous alternatives. Their stability properties are studied in terms of their influence functions and breakdown points. It is shown that the tests have bounded influence functions. For the Wald-type tests, the level and power breakdowns are determined by the breakdown point of the parameter estimate and the associated variance-covariance matrix. The drop-in-dispersion test exhibits high-level breakdown but not high power breakdown point. Similar behavior is exhibited by the score-type tests. But slight modifications can be made in the construction of the test statistics to ensure high breakdown points in terms of both level and power. An example is given to illustrate the usefulness of high-breakdown testing procedures.

Key Words:

• Asymptotic distribution
• Breakdown point
• Influence function
• Robustness
• Testing procedures