zbMATH — the first resource for mathematics

A missing information principle and $$M$$-estimators in regression analysis with censored and truncated data. (English) Zbl 0817.62030
Summary: 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.

MSC:
 62G07 Density estimation 62G35 Nonparametric robustness 62F35 Robustness and adaptive procedures (parametric inference) 62J05 Linear regression; mixed models 60F05 Central limit and other weak theorems 62G20 Asymptotic properties of nonparametric inference
Full Text: