Size and Power of Tests for Regression Outliers in the Forward Search

The Forward Search is a method for detecting masked outliers and for determining their effect on models fitted to the data. We have estimated the actual statistical size and power of the Forward Search in regression through a large number of simulations, for a wide set of sample sizes and several dimensions. Special attention is given here to the statistical size. The work confirms for regression the excellent Forward Search properties shown in the multivariate context by Riani et al. (Journal of the Royal Statistical Society. Series B 71:1–21, 2009).