Open Access
December 1996 Asymptotic equivalence of nonparametric regression and white noise
Lawrence D. Brown, Mark G. Low
Ann. Statist. 24(6): 2384-2398 (December 1996). DOI: 10.1214/aos/1032181159


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.


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Lawrence D. Brown. Mark G. Low. "Asymptotic equivalence of nonparametric regression and white noise." Ann. Statist. 24 (6) 2384 - 2398, December 1996.


Published: December 1996
First available in Project Euclid: 16 September 2002

zbMATH: 0867.62022
MathSciNet: MR1425958
Digital Object Identifier: 10.1214/aos/1032181159

Primary: 62G07
Secondary: 62G20 , 62M05

Keywords: Linear estimators , local asymptotic minimaxity , Risk equivalence

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 6 • December 1996
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