Asymptotic equivalence of nonparametric regression and white noise. (English) Zbl 0867.62022

Summary: The principal result is that, under conditions, to any nonparametric regression problem there corresponds an asymptotically equivalent sequence of white noise with drift problems, and conversely. This asymptotic equivalence is in a global and uniform sense. Any normalized risk function attainable in one problem is asymptotically attainable in the other, with the difference in normalized risks converging to zero uniformly over the entire parameter space. The results are constructive. A recipe is provided for producing these asymptotically equivalent procedures. Some implications and generalizations of the principal result are also discussed.


62G07 Density estimation
62M05 Markov processes: estimation; hidden Markov models
62G20 Asymptotic properties of nonparametric inference
62C99 Statistical decision theory
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