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September, 1994 A Missing Information Principle and $M$-Estimators in Regression Analysis with Censored and Truncated Data
Tze Leung Lai, Zhiliang Ying
Ann. Statist. 22(3): 1222-1255 (September, 1994). DOI: 10.1214/aos/1176325627

Abstract

A general missing information principle is proposed for constructing $M$-estimators of regression parameters in the presence of left truncation and right censoring on the observed responses. By making use of martingale central limit theorems and empirical process theory, the asymptotic normality of $M$-estimators is established under certain assumptions. Asymptotically efficient $M$-estimators are also developed by using data-dependent score functions. In addition, robustness properties of the estimators are discussed and formulas for their influence functions are derived for the robustness analysis.

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Tze Leung Lai. Zhiliang Ying. "A Missing Information Principle and $M$-Estimators in Regression Analysis with Censored and Truncated Data." Ann. Statist. 22 (3) 1222 - 1255, September, 1994. https://doi.org/10.1214/aos/1176325627

Information

Published: September, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0817.62030
MathSciNet: MR1311974
Digital Object Identifier: 10.1214/aos/1176325627

Subjects:
Primary: 62J99
Secondary: 60F05, 62E20, 62G05, 62G35

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 3 • September, 1994
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