缺失数据下异方差半变系数模型的约束统计推断  

Restricted Statistical Inference for Heteroscedastic Semi-varying Coefficient Models with Missing Data

作　　者：张巍巍 萨如拉 冯三营 ZHANG Weiwei;SA Rula;FENG Sanying(College of Science,Inner Mongolia Agricultural University,Hohhot 010018,China;School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]内蒙古农业大学理学院,内蒙古呼和浩特010018 [2]郑州大学数学与统计学院,河南郑州450001

出　　处：《应用数学》2022年第3期617-627,共11页Mathematica Applicata

基　　金：内蒙古自治区高等学校科学技术研究项目(NJSY22497);内蒙古自然科学基金(2020BS01011);河南省自然科学基金(212300410412);河南省高等学校重点科研项目(21A910004)。

摘　　要：本文研究协变量随机缺失下异方差半参数变系数模型约束估计问题.首先在完全数据情形下,利用profile最小二乘方法构造模型参数和非参数分量的约束估计量;其次利用非参数核估计方法构造方差函数的约束估计量;随后基于逆概率加权法和加权profile最小二乘法构造模型参数和非参数分量的自适应逆概率加权profile最小二乘约束估计量;最后在一定正则条件下证明自适应逆概率加权profile最小二乘约束估计量的渐近性质,并通过蒙特卡洛数值模拟验证有限样本表现.In this article,we consider the constrained estimation problem for a heteroscedastic semiparametric varying-coefficient model with covariates missing at random.Firstly,the profile least square method is used to construct the constrained estimators for the parametric and nonparametric components based on complete-case data.Furthermore,we employ the nonparametric kernel estimation method to obtain the constrained estimator of the error variance.And then by combining the inverse probability weighted method and the weighted profile least squares method,the adaptive inverse probability weighted profile least squares constrained estimators for the parametric and nonparametric components are constructed.Finally,the asymptotic properties of the adaptive inverse probability weighted profile least square constrained estimators are proved under certain regularization conditions,and the finite sample performance is illustrated by Monte Carlo simulation.

关 键 词：半变系数模型 异方差 核估计 缺失数据 自适应逆概率加权profile最小二乘方法 

分 类 号：O212.7[理学—概率论与数理统计]