 Department of
StatisticsUniversity of California, Santa Barbara |
ANDREW V. CARTER | |||||||
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Asymptotic approximation of nonparametric regression
experiments with unknown variances. Annals of Statistics 35 pp.
1644-1673.
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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. [Full Paper in .pdf ] [Back to Publications page] [Back to Research page]
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