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Springer, Journal of the Korean Statistical Society, 2(39), p. 153-159, 2010

DOI: 10.1016/j.jkss.2010.04.007

Springer, Journal of the Korean Statistical Society, 2(39), p. 137-145, 2010

DOI: 10.1016/j.jkss.2010.02.003

Springer, Journal of the Korean Statistical Society, 2(39), p. 151, 2010

DOI: 10.1016/j.jkss.2010.02.002

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Discussion: The forward search: Theory and data analysis.

Journal article published in 2010 by Domenico Perrotta, Elvezio Ronchetti, L. A. García-Escudero, Søren Johansen, Bent Nielsen, A. Gordaliza, Vytis Kopustinskas, A. Mayo-Iscar ORCID, Tsung-Chi Cheng
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Abstract

The paper by Atkinson, Riani, and Ceroli (2010), henceforth ARC, is concerned with detection of outliers and unsuspected structures which is rather important in practice. This is done through a Forward Search Algorithm. The statistical analysis of such algorithms poses many challenging problems, and we would like to contribute to the theory of the algorithm in this discussion. We establish some results in a simple case for a single iteration of the algorithm using empirical process theory. This would then have to be extended to more models, and developed further to understand the properties of the full algorithm. The established results suggest that the heuristic results from ARC could be correct if the parameters were known, but not when the parameters are estimated.