  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.
