Open Access
June 2002 Asymptotic equivalence theory for nonparametric regression with random design
Lawrence D. Brown, T. Tony Cai, Mark G. Low, Cun-Hui Zhang
Ann. Statist. 30(3): 688-707 (June 2002). DOI: 10.1214/aos/1028674838


This paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on an unknown regression or drift function. The asymptotic equivalence is established by constructing explicit equivalence mappings between the nonparametric regression and the white-noise experiments, which provide synthetic observations and synthetic asymptotic solutions from any one of the two experiments with asymptotic properties identical to the true observations and given asymptotic solutions from the other. The impact of such asymptotic equivalence results is that an investigation in one nonparametric problem automatically yields asymptotically analogous results in all other asymptotically equivalent nonparametric problems.


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Lawrence D. Brown. T. Tony Cai. Mark G. Low. Cun-Hui Zhang. "Asymptotic equivalence theory for nonparametric regression with random design." Ann. Statist. 30 (3) 688 - 707, June 2002.


Published: June 2002
First available in Project Euclid: 6 August 2002

zbMATH: 1029.62044
MathSciNet: MRAOS30N3R4
Digital Object Identifier: 10.1214/aos/1028674838

Primary: 62G20
Secondary: 62G08

Keywords: ‎asymptotic ‎equivalence , Le Cam's distance , Nonparametric regression , white-noise model

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 3 • June 2002
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