OPTIMAL GLOBAL RATES OF CONVERGENCE OF M-ESTIMATES FOR NONPARAMETRIC REGRESSION

SHI Peide;LI Guoying

系统科学与复杂性(英文) ›› 1995, Vol. 8 ›› Issue (1) : 57-065.

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系统科学与复杂性(英文) ›› 1995, Vol. 8 ›› Issue (1) : 57-065.
论文

OPTIMAL GLOBAL RATES OF CONVERGENCE OF M-ESTIMATES FOR NONPARAMETRIC REGRESSION

    SHI Peide; LI Guoying
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OPTIMAL GLOBAL RATES OF CONVERGENCE OF M-ESTIMATES FOR NONPARAMETRIC REGRESSION

    SHI Peide; LI Guoying
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摘要

Let (X, Y) be a pair of random variables such that X ranges over [0, 1] and Y is real-valued and let go(X) be the conditional expectation of Y given X. Based on a training sample, the piecewise polynomial estimator of go is obtained via usual M-estimates. It is proved that under certain regularity conditions the piecewise polynomial M-estimator achieves the optimal global rate of convergence of estimators for nonparametric regression.

Abstract

Let (X, Y) be a pair of random variables such that X ranges over [0, 1] and Y is real-valued and let go(X) be the conditional expectation of Y given X. Based on a training sample, the piecewise polynomial estimator of go is obtained via usual M-estimates. It is proved that under certain regularity conditions the piecewise polynomial M-estimator achieves the optimal global rate of convergence of estimators for nonparametric regression.

关键词

Nonparametric regression / optimal rate o

Key words

Nonparametric regression / optimal rate of convergencet piecewise polynomial / M-Estimates

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SHI Peide , LI Guoying. OPTIMAL GLOBAL RATES OF CONVERGENCE OF M-ESTIMATES FOR NONPARAMETRIC REGRESSION. 系统科学与复杂性(英文), 1995, 8(1): 57-065
SHI Peide , LI Guoying. OPTIMAL GLOBAL RATES OF CONVERGENCE OF M-ESTIMATES FOR NONPARAMETRIC REGRESSION. Journal of Systems Science and Complexity, 1995, 8(1): 57-065
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