Random Censorship Lost Under The Semi-parametric Regression Model For The Study Of Statistical Properties

Considering the heteroscedastic regression model:yi = xiβ + g(ti) + σiei, σ2i = f(ui) and i=1,2,......, nHere the design points (xi,ti,ui) are known and nonrandom, g, f are unknown functions, and ei is an unobserved disturbance. When the observation of the respond variable yi are case one randomly censored and the censoring distribution function is known, nonparametric estimates ~gn and ~fn is proposed and parametric estimate ~βn is obtained. Under some natural and reasonable conditions, we have:(1) the strong consistency and p(≥2) order mean consistency of the estimators;(2) the asymptotic normality of parametric estimate , the optimal convergence rate of the nonparametric;(3) the generalized model is studied, and the asymptotic normality of parametric estimate , the optimal convergence rate of the nonparametric under multivariable βpx1=(β1,β2,.....,βp)T condition;(4) simulation studies are carried out.