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• W2020201062 abstract "We establish that a non-Gaussian nonparametric regression model is asymptotically equivalent to a regression model with Gaussian noise. The approximation is in the sense of Le Cam's deficiency distance Δ; 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 exponential family. The canonical parameter is a value f(t i ) of a regression function f at a grid point t i (nonparametric GLM). When f is in a Hölder ball with exponent we establish global asymptotic equivalence to observations of a signal Γ(f(t)) in Gaussian white noise, where Γ is related to a variance stabilizing transformation in the exponential family. The result is a regression analog of the recently established Gaussian approximation for the i.i.d. model. The proof is based on a functional version of the Hungarian construction for the partial sum process." @default.
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• W2020201062 date "1998-06-01" @default.
• W2020201062 modified "2023-09-27" @default.
• W2020201062 title "Asymptotic equivalence for nonparametric generalized linear models" @default.
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• W2020201062 doi "https://doi.org/10.1007/s004400050166" @default.
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