The maximum asymptotic bias of S-estimates for regression over the neighborhoods defined by certain special capacities |
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Authors: | Masakazu Ando Miyoshi Kimura |
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Institution: | a Graduate School of Business Administration, Nanzan University, 18 Yamazato-cho, Showa-ku, Nagoya 466-8673, Japan;b Department of Mathematical Sciences, Nanzan University, 27 Seirei-cho, Seto, Aichi 489-0863, Japan |
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Abstract: | The maximum asymptotic bias of an S-estimate for regression in the linear model is evaluated over the neighborhoods (called (c,γ)-neighborhoods) defined by certain special capacities, and its lower and upper bounds are derived. As special cases, the (c,γ)-neighborhoods include those in terms of -contamination, total variation distance and Rieder's (,δ)-contamination. It is shown that when the model distribution is normal and the (,δ)-contamination neighborhood is adopted, the lower and upper bounds of an S-estimate (including the LMS-estimate) based on a jump function coincide with the maximum asymptotic bias. The tables of the maximum asymptotic bias of the LMS-estimate are given. These results are an extension of the corresponding ones due to Martin et al. (Ann. Statist. 17 (1989) 1608), who used -contamination neighborhoods. |
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Keywords: | S-estimate LMS-estimate Robust regression Maximum asymptotic bias sciencedirect com/scidirimg/entities/25b -contamination" target="_blank">gif" alt="var epsilon" title="var epsilon" border="0">-contamination Total variation Special capacity |
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