The Annals of Statistics

Asymptotic approximation of nonparametric regression experiments with unknown variances

Andrew V. Carter

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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.

Article information

Ann. Statist., Volume 35, Number 4 (2007), 1644-1673.

First available in Project Euclid: 29 August 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62B15: Theory of statistical experiments
Secondary: 62G20: Asymptotic properties 62G08: Nonparametric regression

asymptotic equivalence of experiments nonparametric regression variance estimation


Carter, Andrew V. Asymptotic approximation of nonparametric regression experiments with unknown variances. Ann. Statist. 35 (2007), no. 4, 1644--1673. doi:10.1214/009053606000001613.

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