非参数回归模型均值与方差双重变点的估计  

Estimation of Change Point in Mean and Variance of Non-parametric Regression Model

作　　者：胡尧 邓春霞 李丽 HU Yao;DENG Chunxia;LI Li(School of Mathematics and Statistics,Guizhou University,Guiyang,550025,China;Guizhou Provincial Key Laboratory of Public Big Data,Guiyang,550025,China)

机构地区：[1]贵州大学数学与统计学院,贵阳550025 [2]贵州省公共大数据重点实验室,贵阳550025

出　　处：《应用概率统计》2018年第3期251-264,共14页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11661018;11361015);全国统计科学研究项目(批准号:2014LZ46);贵州省自然科学基金项目(黔科合J字[2014]2058号);贵州省科技计划项目(黔科合平台人才[2017]5788号)资助

摘　　要：本文基于核估计和小波方法研究异方差非参数回归模型中均值函数和方差函数均存在变点的估计问题.首先,构造基于均值函数的核估计量,求出均值变点位置及跳跃度的估计.其次,利用小波方法构造方差变点的估计量,运用该估计量获得方差变点位置与跳跃度的估计,给出变点估计量的渐近性质.最后数值模拟并通过比较验证了方法的有效性.This paper studies the estimation of change point in mean and variance function of a non-parametric regression model based on kernel estimation and wavelet method.First,kernel estimation of mean function is developed and it is used to estimate the position and jump size of mean change.Second,wavelet methods are applied to derive the variance estimator which is used to estimate the location and jump size of the change point in variance.The asymptotic properties of these estimators are proved.Finally,the results from a numerical simulations and comparison study show that validate the eectiveness of our method.

关 键 词：变点 小波方法 核估计 非参致回归 

分 类 号：O212.7[理学—概率论与数理统计]