Convergence Rate of Estimator forNonparametric Regression Model under ρ-mixing Errors  

-混合误差下非参数回归模型估计量的收敛速度（英文）

作　　者：ttU Qi HUANG Qian YANG Wen-zhi LI Xiao-qin 

机构地区：[1]School of Mathematical Sciences, Anhui University, Hefei 230601, China

出　　处：《Chinese Quarterly Journal of Mathematics》2017年第4期407-414,共8页数学季刊（英文版）

基　　金：Supported by National Natural Science Foundation of China(11426032,11501005);Natural Science Foundation of Anhui Province(1408085QA02,1508085QA01,1508085J06);Provincial Natural Science Research Project of Anhui Colleges(KJ2014A010,KJ2014A020,KJ2015A065);Higher Education Talent Revitalization Project of Anhui Province(2013SQRL005ZD);Quality Engineering Project of Anhui Province(2015jyxm054,2015jyxm057);Students Science Research Training Program of Anhui University(KYXL2014016,KYXL2014013);Applied Teaching Model Curriculum of Anhui University(XJYYKC1401,ZLTS2015052,ZLTS2015053);Doctoral Research Start-up Funds Projects of Anhui University

摘　　要：In this paper, we investigate the nonparametric regression model based on ρ-mixing errors, which are stochastically dominated by a nonnegative random variable. Weobtain the convergence rate for the weighted estimator of unknown function g（x） in pth-mean, which yields the convergence rate in probability. Moreover, an example of the nearestneighbor estimator is also illustrated and the convergence rates of estimator are presented.In this paper, we investigate the nonparametric regression model based on -mixing errors, which are stochastically dominated by a nonnegative random variable. We obtain the convergence rate for the weighted estimator of unknown function g(x) in pthmean, which yields the convergence rate in probability. Moreover, an example of the nearest neighbor estimator is also illustrated and the convergence rates of estimator are presented.

关 键 词：convergence rate pth-mean Ρ-MIXING sequence NONPARAMETRIC regressionmodel 

分 类 号：O211.4[理学—概率论与数理统计]