Open Access
August 2007 Asymptotic approximation of nonparametric regression experiments with unknown variances
Andrew V. Carter
Ann. Statist. 35(4): 1644-1673 (August 2007). DOI: 10.1214/009053606000001613


Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown nuisance parameter. We establish an asymptotic approximation to the nonparametric regression experiment when the value of the variance is an additional parameter to be estimated or tested. This asymptotically equivalent experiment has two components: the first contains all the information about the variance and the second has all the information about the mean. The result can be extended to regression problems where the variance varies slowly from observation to observation.


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Andrew V. Carter. "Asymptotic approximation of nonparametric regression experiments with unknown variances." Ann. Statist. 35 (4) 1644 - 1673, August 2007.


Published: August 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1147.62034
MathSciNet: MR2351100
Digital Object Identifier: 10.1214/009053606000001613

Primary: 62B15
Secondary: 62G08 , 62G20

Keywords: asymptotic equivalence of experiments , Nonparametric regression , variance estimation

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 4 • August 2007
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