Asymptotic analysis of the Forward Search

The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data.  This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000).  An asymptotic analysis of the Forward Search is made.  The argument involves theory for a new class of weighted and marked empirical processes, quantile process theory, and a fixed point argument to describe the iterative element of the procedure.