Asymptotic equivalence of nonparametric location models

We establish that a non-Gaussian nonparametric regression model is asymptoticaly equivalent to a regression model with Gaussian noise. The approximation is in the sense of Le Cam\u27s deficiency distance $\Delta;$ the models are then asymptotically equivalent for all purposes of statistical decision with bounded loss. Our result concerns a sequence of independent but not identically distributed observations with each distribution in the same real-indexed location family. The canonical parameter is a value $f(t\sb{i})$ of a regression function f at a grid point $t\sb{i}.$ When f is in a Holder ball with exponent $\beta\u3e{1\over2},$ we establish global asymptotic equivalence to observations of a signal $f(t)$ in Gaussian white noise. The proof is based on an application of Edgeworth expansion for partial sums. The results are constructive. A recipe is provided for producing these asymptotically equivalent procedures