Asymptotic Equivalence for Nonparametric Regression

@inproceedings{Nussbaum2002AsymptoticEF,
  title={Asymptotic Equivalence for Nonparametric Regression},
  author={Michael Nussbaum},
  year={2002}
}
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… CONTINUE READING
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