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- W2022370612 abstract "A natural measure of the degree of robustness of an estimate $mathbf{T}$ is the maximum asymptotic bias $B_mathbf{T}(varepsilon)$ over an $varepsilon$-contamination neighborhood. Martin, Yohai and Zamar have shown that the class of least $alpha$-quantile regression estimates is minimax bias in the class of $M$-estimates, that is, they minimize $B_mathbf{T}(varepsilon)$, with $alpha$ depending on $varepsilon$. In this paper we generalize this result, proving that the least $alpha$-quantile estimates are minimax bias in a much broader class of estimates which we call residual admissible and which includes most of the known robust estimates defined as a function of the regression residuals (e.g., least median of squares, least trimmed of squares, $S$-estimates, $tau$-estimates, $M$-estimates, signed $R$-estimates, etc.). The minimax results obtained here, likewise the results obtained by Martin, Yohai and Zamar, require that the carriers have elliptical distribution under the central model." @default.
- W2022370612 created "2016-06-24" @default.
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- W2022370612 date "1993-12-01" @default.
- W2022370612 modified "2023-10-13" @default.
- W2022370612 title "A Minimax-Bias Property of the Least $alpha$-Quantile Estimates" @default.
- W2022370612 doi "https://doi.org/10.1214/aos/1176349400" @default.
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