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Asymptotic equivalence theory for nonparametric regression with random design. (English) Zbl 1029.62044

Summary: This paper establishes the global asymptotic equivalence between nonparametric regression with random design and 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.

MSC:

62G20 Asymptotic properties of nonparametric inference
62G08 Nonparametric regression and quantile regression
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References:

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[14] 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
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