The Annals of Statistics

Optimum robust testing in linear models

Christine Müller

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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.

Article information

Ann. Statist., Volume 26, Number 3 (1998), 1126-1146.

First available in Project Euclid: 21 June 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F35: Robustness and adaptive procedures 62K05
Secondary: 62J05 62J10

Linear model shrinking contamination robust tests asymptotically linear estimators bias of the level most robustness efficiency $D$-optimality optimal design


Müller, Christine. Optimum robust testing in linear models. Ann. Statist. 26 (1998), no. 3, 1126--1146. doi:10.1214/aos/1024691091.

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