BOUNDED INFLUENCE AND HIGH BREAKDOWN POINT TESTING PROCEDURES IN LINEAR-MODELS

Three classes of testing procedures based on one-step high breakdown p oint bounded influence estimators, for testing subhypotheses in linear models are developed. These are drop-in-dispersion, Wald-type, and sc ore-type tests. The asymptotic distributions of these testing procedur es are obtained under the null hypothesis and under contiguous alterna tives. Their stability properties are studied in terms of their influe nce functions and breakdown points. It is shown that the tests have bo unded influence functions. For the Wald-type tests, the level and powe r breakdowns are determined by the breakdown point of the parameter es timate and the associated variance-covariance matrix. The drop-in-disp ersion test exhibits high-level breakdown but not high power breakdown point. Similar behavior is exhibited by the score-type tests. But sli ght modifications can be made in the construction of the test statisti cs to ensure high breakdown points in terms of both level and power. A n example is given to illustrate the usefulness of high-breakdown test ing procedures.