Strong convergence in nonparametric estimation of regression functions

K. F. Cheng

doi:10.1007/BF01855429

Strong convergence in nonparametric estimation of regression functions

K. F. Cheng

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The nonparametric regression problem has the objective of estimating conditional expectation. Consider the model {Mathematical expression}, where the random variable Z has mean zero and is independent of X. The regression function R(x) is the conditional expectation of Y given X = x. For an estimator of the form {Mathematical expression}, we obtain the rate of strong uniform convergence {Mathematical expression}. Here X is a d-dimensional variable and C is a suitable subset of R^d.

Original language	English
Pages (from-to)	177-187
Number of pages	11
Journal	Periodica Mathematica Hungarica
Volume	14
Issue number	2
DOIs	https://doi.org/10.1007/BF01855429
Publication status	Published - Jun 1983
Externally published	Yes

Keywords

AMS (MOS) subject classifications (1970): Primary 62G05, Secondary 60F15
Nonparametric regression
strong convergence

ASJC Scopus subject areas

General Mathematics

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10.1007/BF01855429

Cite this

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title = "Strong convergence in nonparametric estimation of regression functions",

abstract = "The nonparametric regression problem has the objective of estimating conditional expectation. Consider the model \{Mathematical expression\}, where the random variable Z has mean zero and is independent of X. The regression function R(x) is the conditional expectation of Y given X = x. For an estimator of the form \{Mathematical expression\}, we obtain the rate of strong uniform convergence \{Mathematical expression\}. Here X is a d-dimensional variable and C is a suitable subset of Rd.",

keywords = "AMS (MOS) subject classifications (1970): Primary 62G05, Secondary 60F15, Nonparametric regression, strong convergence",

author = "Cheng, \{K. F.\}",

year = "1983",

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AU - Cheng, K. F.

PY - 1983/6

Y1 - 1983/6

N2 - The nonparametric regression problem has the objective of estimating conditional expectation. Consider the model {Mathematical expression}, where the random variable Z has mean zero and is independent of X. The regression function R(x) is the conditional expectation of Y given X = x. For an estimator of the form {Mathematical expression}, we obtain the rate of strong uniform convergence {Mathematical expression}. Here X is a d-dimensional variable and C is a suitable subset of Rd.

AB - The nonparametric regression problem has the objective of estimating conditional expectation. Consider the model {Mathematical expression}, where the random variable Z has mean zero and is independent of X. The regression function R(x) is the conditional expectation of Y given X = x. For an estimator of the form {Mathematical expression}, we obtain the rate of strong uniform convergence {Mathematical expression}. Here X is a d-dimensional variable and C is a suitable subset of Rd.

KW - AMS (MOS) subject classifications (1970): Primary 62G05, Secondary 60F15

KW - Nonparametric regression

KW - strong convergence

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U2 - 10.1007/BF01855429

DO - 10.1007/BF01855429

M3 - Article

AN - SCOPUS:34250150873

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JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

IS - 2

ER -

Strong convergence in nonparametric estimation of regression functions

Abstract

Keywords

ASJC Scopus subject areas

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