Asymptotic Equivalence Theory For Nonparametric Regression With Random Noise
The Annals of Statistics 30, 688-707, (2002).

Lawrence Brown, Tony Cai, Mark Low and Cun-Hui Zhang

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• Abstract: This paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on the unknown regression/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 identical asymptotic properties 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.

• Paper: pdf file.