Efficient Score Estimation and Adaptive Rank and M-estimators from Left-Truncated and Right-Censored Data

  • Chul-Ki Kim (Assistant Professor, Department of Statistics, Ewha Womans University, Seoul, 120-750 , Korea)
  • Published : 1996.12.01

Abstract

Data-dependent (adaptive) choice of asymptotically efficient score functions for rank estimators and M-estimators of regression parameters in a linear regression model with left-truncated and right-censored data are developed herein. The locally adaptive smoothing techniques of Muller and Wang (1990) and Uzunogullari and Wang (1992) provide good estimates of the hazard function h and its derivative h' from left-truncated and right-censored data. However, since we need to estimate h'/h for the asymptotically optimal choice of score functions, the naive estimator, which is just a ratio of estimated h' and h, turns out to have a few drawbacks. An altermative method to overcome these shortcomings and also to speed up the algorithms is developed. In particular, we use a subroutine of the PPR (Projection Pursuit Regression) method coded by Friedman and Stuetzle (1981) to find the nonparametric derivative of log(h) for the problem of estimating h'/h.

Keywords

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