Asymptotic approximation of nonparametric regression experiments with unknown variances

Details Asymptotic approximation of nonparametric regression experiments with unknown variances Asymptotic approximation of nonparametric regression experiments with unknown variances

2007-10-19

arxiv.org/abs/0710.3647v1

Annals of Statistics 2007, Vol. 35, No. 4, 1644-1673

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053606000001613 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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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