The Annals of Statistics

Asymptotic equivalence theory for nonparametric regression with random design

Lawrence D. Brown, T. Tony Cai, Mark G. Low, and Cun-Hui Zhang

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 30, Number 3 (2002), 688-707.

Dates
First available in Project Euclid: 6 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1028674838

Digital Object Identifier
doi:10.1214/aos/1028674838

Mathematical Reviews number (MathSciNet)
MRaos30n3r4

Zentralblatt MATH identifier
1029.62044

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62G08: Nonparametric regression

Keywords
Asymptotic equivalence Le Cam's distance nonparametric regression white-noise model

Citation

Brown, Lawrence D.; Cai, T. Tony; Low, Mark G.; Zhang, Cun-Hui. Asymptotic equivalence theory for nonparametric regression with random design. Ann. Statist. 30 (2002), no. 3, 688--707. doi:10.1214/aos/1028674838. https://projecteuclid.org/euclid.aos/1028674838


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References

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  • PHILADELPHIA, PENNSy LVANIA 19104 E-MAIL: lbrown@wharton.upenn.edu T. T. CAI DEPARTMENT OF STATISTICS THE WHARTON SCHOOL UNIVERSITY OF PENNSy LVANIA
  • PHILADELPHIA, PENNSy LVANIA 19104 E-MAIL: tcai@wharton.upenn.edu M. G. LOW DEPARTMENT OF STATISTICS THE WHARTON SCHOOL UNIVERSITY OF PENNSy LVANIA
  • PHILADELPHIA, PENNSy LVANIA 19104 C.-H. ZHANG DEPARTMENT OF STATISTICS RUTGERS UNIVERSITY
  • PISCATAWAY, NEW JERSEY 08854