Abstract
Abstract Let us consider the linear model Y = Xθ + E in the usual matrix notation, where the errors are iid. Our main objective is to develop robust Wald-type tests for a large class of hypotheses on θ; by robust we mean robustness in terms of size and power against long-tailed error distributions. First assume that the error distribution is symmetric about the origin. Let L and be the least squares and a robust estimator of θ. Assume that they are asymptotically normal about θ with covariance matrices σ 2(XtX)–1 and τ 2(XtX)–1, respectively. So could be an M estimator or a high breakdown point estimator. Robust Wald-type tests based on (denoted by RW) are studied here for testing a large class of one-sided hypotheses on θ. It is shown that the asymptotic null distribution of RW and that of the usual Wald-type statistic based on L (denoted by W) are the same. This is a useful result since the critical values and procedures for computing the p values for W are directly applicable to RW as well. A more impo...
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