Breakdown points for designed experiments

Abstract

For designed experiments we define the breakdown point of an estimator without allowing contaminated experimental conditions (explanatory, independent variables) because they are given by a fixed design. This provides a different definition of the breakdown point as it was used in former literature. For a wide class of estimators which we call h-trimmed weighted L p estimators and which includes high breakdown point estimators as the LMS estimator and the LTS estimators among others, we derive the breakdown point for situations which often appear in designed experiments. In particular, we derive the breakdown point for replicated experimental conditions and show that a design which maximizes the breakdown point should minimize the maximal number of experimental conditions which lie in a subspace of the parameter space. This provides a new optimality criterion for designs. This new optimality criterion leads to designs which are very different from the classical optimal designs. Two examples demonstrate the different behaviour.