伪可加模型的稳健估计  

Robust Estimation of Quasi-Additive Model

作　　者：李建涛[1] 郑敏[1] 刘艳玲[1] 

机构地区：[1]北京大学数学科学学院,北京100871

出　　处：《数学学报（中文版）》2009年第2期323-336,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10471006)

摘　　要：针对伪可加模型,本文利用局部线性回归和边缘积分的方法提出了一种稳健的估计方法.在一些正规性条件之下,证明了估计量是存在的且是渐近正态的.为了降低估计量的计算负担,提出了一步局部M-估计量.在初始值足够好的情形下,证明了一步局部M-估计量与完全迭代的M-估计量具有相同的渐近分布.换言之,一步局部M-估计量继承了完全迭代估计量的优良性质,但却大大降低了计算负担.以上事实将通过数值模拟来给予说明.A robust estimation method of the components of quasi-additive model using local linear regression and marginal integration is studied. Robust estimators are proposed for estimating the quasi-additive components. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotic normal. Based on the robust estimation equations, one-step approximation to the fully-iterative M-estimator is introduced to reduce computational burden. The one-step estimator is shown to share the same asymptotic distribution as the fully-iterative M-estimator as long as the initial estimator is good enough. In other words, the one-step local M- estimator reduce significantly the computation cost of the fully-iterative M-estimator without deteriorating its performance. These facts are illustrated via numerical simulations.

关 键 词：局部 M-估计量 边缘积分 伪可加模型 

分 类 号：O212.7[理学—概率论与数理统计]