Asymptotic Equivalence Theory for Nonparametric Regression with Random Design
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.