Optimum robust testing in linear models

• 成果类型: Article
• 署名作者: Müller, C
• 署名单位: University of Gottingen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1126-1146
• 关键词: bounded-influence tests; one-sided hypotheses; regression models; designs

摘要

Robust tests for Linear models are derived via Wald-type tests that are based on asymptotically linear estimators. For a robustness criterion, the maximum asymptotic bias of the level of the test for distributions in a shrinking contamination neighborhood is used. By also regarding the asymptotic power of the test, admissible robust tests and most-efficient robust tests are derived. For the greatest efficiency, the determinant of the covariance matrix of the underlying estimator is minimized. Also, most-robust tests are derived. It is shown that at the classical D-optimal designs, the most-robust tests and the most-efficient robust tests have a very simple form. Moreover, the D-optimal designs provide the highest robustness and the highest efficiency under robustness constraints across all designs. So, D-optimal designs are also the optimal designs for robust testing. Two examples are considered for which the most-robust tests and the most-efficient robust tests are given.