部分线性单指标模型的两步M-估计的大样本性质

Asymptotic Properties of Two-step M-estimators in a Partial Linear Single-index Model

单指标模型是一类非常重要的非参数多元回归模型,不仅可以降低数据维数,而且能抓住高维数据的主要特征.本文研究部分线性单指标模型的参数的M-估计,利用局部多项式近似技术,提出了获得模型中未知参数的两步M-估计方法,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-估计的渐近性质,利用随机模拟方法,研究了估计的小样本性质.

The single-index model is an important tool in multivariate nonparametric regression. It not only can reduce the dimension of data, but also can capture the main feature of data. This paper deals with M-estimators for the partial linear single-index model. A two-step estimates procedure based on local linear polynomial approximation is proposed.Under some mild regular conditions, the asymptotic properties of the proposed M-estimators of unknown function and its derivative and the M-estimator of parameter is investigated. The finite sample properties of the estimation is considered by a random simulation study.