DMCA
Nonparametric regression with errors in variables (1993)
| Venue: | Annals of Statistics |
| Citations: | 84 - 1 self |
BibTeX
@ARTICLE{Fan93nonparametricregression,
author = {Jianqing Fan and Young K. Truong},
title = {Nonparametric regression with errors in variables},
journal = {Annals of Statistics},
year = {1993},
pages = {1900--1925}
}
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Abstract
The effect of errors in variables in nonparametric regression estimation is examined. To account for errors in covariates, deconvolution is involved in the construction ofa new class of kernel estimators. It is shown that optima/local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution. In fact, there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth. It is also shown that these results hold uniformly over a class of joint distributions of the response and the covariates, which includes ordinary smooth regression functions as well as covariates with distributions satisfying regularity conditions. Furthermore, to achieve optimality, we show that the convergence rates of all nonparametric estimators have a lower bound possessed by the kernel estimators. oAbbreviated title. Error-in-variable regression AMS 1980 subject classification. Primary 62G20. Secondary 62G05, 62J99. Key words and phrases. Nonparametric regression; Kernel estimator; Errors in variables; Optimal rates
Keyphrases
kernel estimator nonparametric regression ordinary smooth super smooth subject classification new class optimal rate convergence rate nonparametric regression estimation characteristic function nonparametric estimator key word joint distribution ordinary smooth regression function error-in-variable regression am global rate error distribution regularity condition tail behavior
