Optimal, robust R-estimators and test statistics in the linear model

Yu Wang and Douglas Wiens

Statistics & Probability Letters, 1992, vol. 14, issue 3, 179-188

Abstract: We consider R-estimation in the linear model, with an eye to obtaining those estimators, and associated test statistics, which are optimal according to certain criteria. We obtain: (a) optimal B-robust estimators, which minimize the asymptotic variance at a fixed distribution, subject to a bound on the influence function of the estimate; (b) optimal B-robust test statistics, which maximize the minimum power of the test, subject to a bound on the influence function of the test; (c) minimax estimators (resp., maximin test statistics), which minimize the maximum variance (resp., maximize the minimum power), as the true distribution of the errors varies over a neighbourhood of the assumed error distribution. Several such estimators are compared, in a Monte Carlo study.

Keywords: Robust; methods; R-estimation; minimax; variance; bounded; influence; B-robust (search for similar items in EconPapers)
Date: 1992
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