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September, 1985 Rate of Convergence of One- and Two-Step $M$-Estimators with Applications to Maximum Likelihood and Pitman Estimators
P. Janssen, J. Jureckova, N. Veraverbeke
Ann. Statist. 13(3): 1222-1229 (September, 1985). DOI: 10.1214/aos/1176349666

Abstract

A one-step version $M^{(1)}_n$ and a two-step version $M^{(2)}_n$ of a general $M$-estimator $M_n$ are suggested such that $M_n - M^{(1)}_n = O_p(n^{-1})$ and $M_n - M^{(2)}_n = O_p(n^{-3/2})$ for every $n^{1/2}$-consistent initial estimator and under some regularity conditions. In the special case of maximum likelihood estimation, this among other yields that the second-order efficiency properties of $M^{(2)}_n$ coincide with those of $M_n$. An application to the Pitman estimator of location is considered.

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P. Janssen. J. Jureckova. N. Veraverbeke. "Rate of Convergence of One- and Two-Step $M$-Estimators with Applications to Maximum Likelihood and Pitman Estimators." Ann. Statist. 13 (3) 1222 - 1229, September, 1985. https://doi.org/10.1214/aos/1176349666

Information

Published: September, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0585.62057
MathSciNet: MR803768
Digital Object Identifier: 10.1214/aos/1176349666

Subjects:
Primary: 62F12
Secondary: 62G05

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 3 • September, 1985
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