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A comparison between several one-step M-estimators of location and dispersion in the presence of a nuisance parameter

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Title: A comparison between several one-step M-estimators of location and dispersion in the presence of a nuisance parameter
Author: Rainville, Eve
Degree Master of Science - MSc
Program Statistics
Copyright Date: 1996
Abstract: The idea of one-step estimators has long been used: Le Cam (1956), Neyman (1949) and Fisher (1922) have proposed it in the context of maximum likelihood estimation. More recently, Bickel (1975) adapted this idea to robustness theory when he introduced one-step Huber M-estimators for simple linear models. Huber (1981) and Hampel et al (1986) further investigated the advantages of such one-step M-estimators; while retaining the robustness properties of their initial estimates, one-step M-estimators show increased efficiency, and thus represent a good compromise between robust and parametric estimation. Different versions of one-step M-estimators, some more numerically stable than others, have been proposed throughout the years. To our knowledge, no thorough comparison of available one-step M-estimators have been done using modern techniques, as in Rousseeuw and Croux (1993a). In this thesis, two versions of one-step M-estimators of location, obtained with the Newton-Raphson method, are studied in the context of unknown dispersion. Their asymptotic efficiencies at Gaussian and non-Gaussian models, as well as their maximum asymptotic bias are compared. We also introduce two new one-step M-estimators of dispersion with unknown location, and challenge the traditional fixed-point method one-step M-estimator of dispersion, originating from Huber (1981) and used by Rousseeuw and Croux (1993a). We identify the optimal situations in which to use any of those three one-step M-estimators of dispersion, using their relative asymptotic efficiency at different models, and their explosion and implosion maximum asymptotic bias curves.
URI: http://hdl.handle.net/2429/4557
Series/Report no. UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/]

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