Optimum robust testing in linear models

Müller, Christine

Ann. Statist., Tome 26 (1998) no. 3, p. 1126-1146 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1998-06-14
Classification:  Linear model,  shrinking contamination,  robust tests,  asymptotically linear estimators,  bias of the level,  most robustness,  efficiency,  $D$-optimality,  optimal design,  62F35,  62K05,  62J05,  62J10