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

Asymptotic approximation of nonparametric regression experiments with unknown variances