一种Sieve极大似然估计的渐近性质

Asymptotic Properties of a Kind of Sieve MLE

该文针对部分线性模型，在响应变量的观测值为Ⅰ型区间删失数据的情形下，讨论Ｓｉｅｖｅ极大似然估计的渐近性质．用三角级数来构造Ｓｉｅｖｅ空间，在一定条件下证明了该估计具有强相合性；得到了该估计的弱收敛速度，并且非参数部分的估计达到了最优收敛速度；还算出了参数部分的信息界．

For a partly linear model, when observations of the respond variable are case one interval censored, asymptotic properties of sieve MLEs are discussed. Triangle series are used to struct sieve spaces, under mild conditions, sieve MLEs are shown to be strong consistent, sieve MLE of the nonparametric part has an optimal convergence rate, and the information bound of sieve MLE of the parametric part is obtained.