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Müller, Christine

Optimum robust testing in linear models. (English) Zbl 0929.62080

Ann. Stat. 26, No. 3, 1126-1146 (1998).
Summary: 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.

Cited in 2 Documents

MSC:

62K05 Optimal statistical designs
62F35 Robustness and adaptive procedures (parametric inference)
62J05 Linear regression; mixed models
62J10 Analysis of variance and covariance (ANOVA)

Keywords:

shrinking contamination; asymptotically linear estimators; bias of level; most robustness; efficiency; D-optimality; linear models; robust tests
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