测量误差数据下单指标模型的非参数模拟外推估计  

Non-parametric Simulation Extrapolation Estimation of Single Index Model for Measurement Error Data

作　　者：王浩 赵培信[1,2] WANG Hao;ZHAO Peixin(College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067;Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring,Chongqing 400067)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]统计智能计算与监测重庆市重点实验室,重庆400067

出　　处：《绵阳师范学院学报》2025年第2期9-15,共7页Journal of Mianyang Teachers' College

基　　金：国家社会科学基金项目(18BTJ035);重庆市自然科学基金项目(cstc2020jcyj-msxmX0006)。

摘　　要：研究了测量误差数据下一类单指标模型的估计问题.结合局部线性平滑法和核密度估计法,提出一种基于非参数模拟外推的模型估计方法 .所提出的非参数模拟外推估计,不需要假定观测变量的具体分布并且不需要假定测量误差的方差已知,具有较广的适应性.在一些正则条件下,证明了非参数模拟外推方法给出的参数估计量的渐近正态性.The estimation problem of a single-index model under the measurement error data is studied.By combining local linear smoothing method and kernel density estimation method,a model estimation method based on non-parametric simulation extrapolation is proposed.The proposed non-parametric simulation extrapolation esti-mate does not need to assume the specific distribution of the observed variables and the variance of the measure-ment error is known,so it has a wide adaptability.Under some regular conditions,the asymptotic normality of the parameter estimators given by the non-parametric simulation extrapolation method is proven.

关 键 词：单指标模型 测量误差数据 核密度函数 非参数模拟外推 

分 类 号：O212[理学—概率论与数理统计]