Statistica Sinica 10(2000), 731-749

EFFICIENT SCORE ESTIMATION AND

ADAPTIVE M-ESTIMATORS IN CENSORED AND

TRUNCATED REGRESSION MODELS

Chul-Ki Kim and Tze Leung Lai

Ewha Womans University and Stanford University

Abstract: An adaptive $M$-estimator of a regression parameter based on censored and truncated data is developed by using $B$-splines to estimate the efficient score function and a relatively simple cross validation method to determine the number of knots. An iterative algorithm to compute the estimator is also provided. The adaptive estimator is asymptotically efficient, and simulation studies of the finite-sample performance of the adaptive estimator shows that it is superior to other $M$-estimators for regression analysis of censored and truncated data in the literature. An asymptotic theory of cross validation in the presence of censoring and truncation is also developed in this connection.

Key words and phrases: Adaptation, B-splines, cross validation, censoring, truncation, efficient estimation.