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September, 1992 Bootstrapping $M$-Estimators of a Multiple Linear Regression Parameter
Soumendra Nath Lahiri
Ann. Statist. 20(3): 1548-1570 (September, 1992). DOI: 10.1214/aos/1176348784

Abstract

Consider a multiple linear regression model $Y_i = x'_i\beta + \varepsilon_i$, where the $\varepsilon_i$'s are independent random variables with common distribution $F$ and the $x_i$'s are known design vectors. Let $\bar\beta_n$ be the $M$-estimator of $\beta$ corresponding to a score function $\psi$. Under some conditions on $F, \psi$ and the $x_i$'s, two-term Edgeworth expansions for the distributions of standardized and studentized $\bar\beta_n$ are obtained. Furthermore, it is shown that the bootstrap method is second order correct in the studentized case when the bootstrap samples are drawn from some suitable weighted empirical distribution or from the ordinary empirical distribution of the residuals.

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Soumendra Nath Lahiri. "Bootstrapping $M$-Estimators of a Multiple Linear Regression Parameter." Ann. Statist. 20 (3) 1548 - 1570, September, 1992. https://doi.org/10.1214/aos/1176348784

Information

Published: September, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0792.62058
MathSciNet: MR1186265
Digital Object Identifier: 10.1214/aos/1176348784

Subjects:
Primary: 62G05
Secondary: 62E20

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 3 • September, 1992
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