随机设计截断半参数模型中估计的渐近性

Asymptotic Properties of Estimators in a Censored Semi-parametric Model Under Random Design

考虑一类新的半参数回归模型Yi=xiβ+g(ti)+σiei,i=1,2,…,n,σ2i=f(ui),其中ti为随机设计点列,Yi被随机右截断.将截断样本数据转化为完全样本数据后,用权函数和两阶段最小二乘方法得到了β,g的估计量.在适当的条件下,研究了参数分量β的估计的渐近正态性和非参数分量g的收敛速度,从而丰富了半参数模型的估计理论,并使其应用性更广泛.

We consider a new semi - parametric regression model ：Yi=xiβ＋g（ti）＋σiei,i=1,2…,n,σi^2=f（ui）,with random design points {ti }, where observations of the respond variable are case one ran- domly - censored. After transforming the case one randomly - censored data into the corresponding completely data, we obtain the estimators of β and g by weight function and two - stage least squares method and derive, under proper conditions, the asymptotic normality of the estimator of β and a convergence rate for the nonparametric part, which enriches the existing estimation theory for semi - parametric regression model and broadens the application.