Asymptotic nonequivalence of nonparametric experiments when the smoothness index is 1/2

Lawrence D. Brown; Cun Hui Zhang

Asymptotic nonequivalence of nonparametric experiments when the smoothness index is 1/2

Lawrence D. Brown, Cun Hui Zhang

School of Arts and Sciences, Statistics

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

27 Scopus citations

Abstract

An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric regression, when the smoothness index of the unknown nonparametric function class is 1/2.

Original language	English (US)
Pages (from-to)	279-287
Number of pages	9
Journal	Annals of Statistics
Volume	26
Issue number	1
State	Published - Feb 1998

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Density estimation
Nonparametric regression
Risk equivalence
White noise

Cite this

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title = "Asymptotic nonequivalence of nonparametric experiments when the smoothness index is 1/2",

abstract = "An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric regression, when the smoothness index of the unknown nonparametric function class is 1/2.",

keywords = "Density estimation, Nonparametric regression, Risk equivalence, White noise",

author = "Brown, {Lawrence D.} and Zhang, {Cun Hui}",

year = "1998",

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volume = "26",

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journal = "Annals of Statistics",

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AU - Zhang, Cun Hui

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AB - An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric regression, when the smoothness index of the unknown nonparametric function class is 1/2.

KW - Density estimation

KW - Nonparametric regression

KW - Risk equivalence

KW - White noise

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JO - Annals of Statistics

JF - Annals of Statistics

IS - 1

ER -

Asymptotic nonequivalence of nonparametric experiments when the smoothness index is 1/2

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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