Analysis of the Forward Search using some new results for martingales and empirical processes

Søren Johansen; Bent Nielsen

doi:10.3150/14-bej689

Analysis of the Forward Search using some new results for martingales and empirical processes

13 Citations (Scopus)

Abstract

The Forward Search is an iterative algorithm for avoiding outliers in a regression analysis suggested by Hadi and Simonoff (J. Amer. Statist. Assoc. 88 (1993) 1264-1272), see also Atkinson and Riani (Robust Diagnostic Regression Analysis (2000) Springer). The algorithm constructs subsets of "good" observations so that the size of the subsets increases as the algorithm progresses. It results in a sequence of regression estimators and forward residuals. Outliers are detected by monitoring the sequence of forward residuals. We show that the sequences of regression estimators and forward residuals converge to Gaussian processes. The proof involves a new iterated martingale inequality, a theory for a new class of weighted and marked empirical processes, the corresponding quantile process theory, and a fixed point argument to describe the iterative aspect of the procedure.

Original language	English
Journal	Bernoulli
Volume	22
Issue number	2
Pages (from-to)	1131-1183
Number of pages	53
ISSN	1350-7265
DOIs	https://doi.org/10.3150/14-bej689
Publication status	Published - May 2016

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Analysis of the Forward Search using some new results for martingales and empirical processes

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