## The Annals of Statistics

### Optimum robust testing in linear models

Christine Müller

#### Abstract

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

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

Dates
First available in Project Euclid: 21 June 2002

https://projecteuclid.org/euclid.aos/1024691091

Digital Object Identifier
doi:10.1214/aos/1024691091

Mathematical Reviews number (MathSciNet)
MR1635454

Zentralblatt MATH identifier
0929.62080

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

#### Citation

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

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