High Robustness and High Efficiency of Tests

Abstract

In this chapter we regard tests based on ALE-test statistics as defined in Section 6.2. In Section 8.1 we characterize “most robust” ALE-tests in linear models, which are ALE-tests with minimum asymptotic bias of the first error for shrinking contamination. We also characterize designs which minimize the asymptotic bias of the first error. In Section 8.2 we characterize admissible ALE-tests and ALE-tests which minimize the determinant of the asymptotic covariance matrix within all ALE-tests with an asymptotic bias of the first error bounded by some bias bound b. Also optimal designs for optimal robust testing are derived. Thereby, in both sections we assume that the ideal model is a homoscedastic linear model with normally distributed errors, i.e. the error Z_nN at t_nN is distributed according to the normal distribution n(0, σ²) with mean 0 and variance $\sigma (t_nN)^2=\sigma ^2\epsilon \mathbb{R}^+$ for all $n=1,...N,\;N\;\epsilon\;\mathbb{N}$. In particular, we have $P=n_{(0,1)}$.