Date of this Version
The Annals of Statistics
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.
risk equivalence, local asymptotic minimaxity, linear estimators
Brown, L. D., & Low, M. G. (1996). Asymptotic Equivalence of Nonparametric Regression and White Noise. The Annals of Statistics, 24 (6), 2384-2398. http://dx.doi.org/10.1214/aos/1032181159
Date Posted: 27 November 2017
This document has been peer reviewed.