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June 1998 Optimum robust testing in linear models
Christine Müller
Ann. Statist. 26(3): 1126-1146 (June 1998). DOI: 10.1214/aos/1024691091


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.


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Christine Müller. "Optimum robust testing in linear models." Ann. Statist. 26 (3) 1126 - 1146, June 1998.


Published: June 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0929.62080
MathSciNet: MR1635454
Digital Object Identifier: 10.1214/aos/1024691091

Primary: 62F35, 62K05
Secondary: 62J05, 62J10

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 3 • June 1998
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