纵向数据下部分线性单指标模型M-估计的大样本性质

Asymptotic character of M-estimation of partially linear single-index model for longitudinal data analysis

针对纵向数据下部分线性单指标模型的参数估计问题以及未知连接函数的估计问题,提出了一种稳健的对单指标部分和线性部分参数同时进行估计的M-估计方法,对未知连接函数做局部多项式估计,在一些正则条件下,研究了回归函数及其导数以及回归系数的M-估计的渐进性质,利用随机模拟方法,验证了所提方法的有效性.

Aimed at the problem of the parameter estimation of partial linear single-index model for longitudinal data and the estimation of the unknown connection function,a robust M-estimation method is proposed for simultaneously estimating the parameters in single-index part and linear part,and a method for estimating local polynomial of unknown connection function is also presented.The asymptotic property of the M-estimation of the regression function and its derivative and the regression coefficient are studied under some regular conditions.The stochastic simulation method is used to illustrate the time-effectiveness of the proposed method and a conclusion is come to that this M-estimation has a large-specimen character.