Asymptotic Equivalence for Nonparametric Regression
نویسنده
چکیده
We consider a nonparametric model E, generated by independent observations Xi, i = 1, ..., n, with densities p(x, θi), i = 1, ..., n, the parameters of which θi = f(i/n) ∈ Θ are driven by the values of an unknown function f : [0, 1]→ Θ in a smoothness class. The main result of the paper is that, under regularity assumptions, this model can be approximated, in the sense of the Le Cam deficiency pseudodistance, by a nonparametric Gaussian shift model Yi = Γ(f(i/n)) + εi, where ε1, ..., εn are i.i.d. standard normal r.v.’s, the function Γ(θ) : Θ → R satisfies Γ′(θ) = √ I(θ) and I(θ) is the Fisher information corresponding to the density p(x, θ).
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