Convergence Rate of Estimator for Nonparametric Regression Model under&nbsp;\widetide{p}-mixing Errors

HU Qi, HUANG Qian, YANG Wen-zhi, LI Xiao-qin

doi:10.13371/j.cnki.chin.q.j.m.2017.04.007

Chinese Quarterly Journal of Mathematics >

2017 , Vol. 32 >Issue 4: 407 - 414

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.04.007

Convergence Rate of Estimator for Nonparametric Regression Model under \widetide{p}-mixing Errors

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School of Mathematical Sciences, Anhui University

HU Qi(1993-), female, native of Tongcheng, Anhui, engages in probability limit theorem; Li Xiao-qin (1983-), female, native of Qianshan, Anhui, a lecturer of Anhui University, Ph.D., engages in probability limit theorem.

Received date: 2015-08-29

Online published: 2020-10-20

Supported by

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；

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Abstract

In this paper, we investigate the nonparametric regression model based on ?ρ-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.

Key words： convergence rate; pth-mean; p^~-mixing sequence; nonparametric regression model

Cite this article

HU Qi, HUANG Qian, YANG Wen-zhi, LI Xiao-qin . Convergence Rate of Estimator for Nonparametric Regression Model under \widetide{p}-mixing Errors[J]. Chinese Quarterly Journal of Mathematics, 2017 , 32(4) : 407 -414 . DOI: 10.13371/j.cnki.chin.q.j.m.2017.04.007

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