## The Annals of Statistics

### A Missing Information Principle and $M$-Estimators in Regression Analysis with Censored and Truncated Data

#### 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.

#### Article information

Source
Ann. Statist., Volume 22, Number 3 (1994), 1222-1255.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325627

Digital Object Identifier
doi:10.1214/aos/1176325627

Mathematical Reviews number (MathSciNet)
MR1311974

Zentralblatt MATH identifier
0817.62030

JSTOR
Lai, Tze Leung; Ying, Zhiliang. A Missing Information Principle and $M$-Estimators in Regression Analysis with Censored and Truncated Data. Ann. Statist. 22 (1994), no. 3, 1222--1255. doi:10.1214/aos/1176325627. https://projecteuclid.org/euclid.aos/1176325627