Configural Polysampling

Abstract

Configural polysampling refers to the estimation and optimization of (small sample) mean-squared-errors in a conditional manner and under a variety of sampling distributions. By including a heavy-tailed distribution along with the Gaussian in the collection of sampling distributions, inference procedures that are robust against heavy-tailed deviations from the Gaussian are obtained. The conditional point of view we referred to, can - and should - be taken whenever ancillary statistics are available. In the case of linear models, where robust techniques seem most urgently needed, such a configural polysampling approach is applicable.

In this paper, this small sample approach to robustness problems is outlined. The exposition has three goals. First, to explain the ideas and calculations that underlie this new approach, and, second, to discuss the interconnections with other schools of robustness. Finally, by application to a concrete problem, namely the rejection of outliers, the practical use of the idea is to be demonstrated.