Open Access
June 1996 On nonparametric regression for IID observations in a general setting
Sam Efromovich
Ann. Statist. 24(3): 1126-1144 (June 1996). DOI: 10.1214/aos/1032526960


We consider the problem of sharp-optimal estimation of a response function $f(x)$ in a random design nonparametric regression under a general model where a pair of observations $(Y, X)$ has a joint density $p(y, x) = p(y|f(x)) \pi(x)$. We wish to estimate the response function with optimal minimax mean integrated squared error convergence as the sample size tends to $\infty$. Traditional regularity assumptions on the conditional density $p(y| \theta)$ assumed for parameter $\theta$ estimation are sufficient for sharp-optimal nonparametric risk convergence as well as for the existence of the best constant and rate of risk convergence. This best constant is a nonparametric analog of Fisher information. Many examples are sketched including location and scale families, censored data, mixture models and some well-known applied examples. A sequential approach and some aspects of experimental design are considered as well.


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Sam Efromovich. "On nonparametric regression for IID observations in a general setting." Ann. Statist. 24 (3) 1126 - 1144, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0865.62025
MathSciNet: MR1401841
Digital Object Identifier: 10.1214/aos/1032526960

Primary: 62G05
Secondary: 62E20 , 62F35 , 62G20 , 62J02

Keywords: Censored data , curves estimation , location and scale families , mixtures , Nonparametric regression , sequential estimation , sharp-optimal risk convergence

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
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