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Partial deconvolution estimation in nonparametric regression
Author(s) -
Shi Jianhong,
Bai Xiuqin,
Song Weixing
Publication year - 2020
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11546
Subject(s) - estimator , deconvolution , nonparametric regression , nonparametric statistics , kernel (algebra) , mathematics , regression function , kernel regression , convergence (economics) , statistics , rate of convergence , covariate , kernel density estimation , regression , computer science , combinatorics , computer network , channel (broadcasting) , economics , economic growth
In this article, we propose a class of partial deconvolution kernel estimators for the nonparametric regression function when some covariates are measured with error and some are not. The estimation procedure combines the classical kernel methodology and the deconvolution kernel technique. According to whether the measurement error is ordinarily smooth or supersmooth, we establish the optimal local and global convergence rates for these proposed estimators, and the optimal bandwidths are also identified. Furthermore, lower bounds for the convergence rates of all possible estimators for the nonparametric regression functions are developed. It is shown that, in both the super and ordinarily smooth cases, the convergence rates of the proposed partial deconvolution kernel estimators attain the lower bound. The Canadian Journal of Statistics 48: 535–560; 2020 © 2020 Statistical Society of Canada