The Annals of Statistics

Asymptotic equivalence of nonparametric regression and white noise

Lawrence D. Brown and Mark G. Low

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist. Volume 24, Number 6 (1996), 2384-2398.

Dates
First available in Project Euclid: 16 September 2002

Permanent link to this document
http://projecteuclid.org/euclid.aos/1032181159

Digital Object Identifier
doi:10.1214/aos/1032181159

Mathematical Reviews number (MathSciNet)
MR1425958

Zentralblatt MATH identifier
0867.62022

Subjects
Primary: 62G07: Density estimation
Secondary: 62G20: Asymptotic properties 62M05: Markov processes: estimation

Keywords
Risk equivalence local asymptotic minimaxity linear estimators

Citation

Brown, Lawrence D.; Low, Mark G. Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 24 (1996), no. 6, 2384--2398. doi:10.1214/aos/1032181159. http://projecteuclid.org/euclid.aos/1032181159.


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