Asymptotic Equivalence Theory for Nonparametric Regression with Random Design by Lawrence

Asymptotic Equivalence Theory for Nonparametric Regression With Random Design

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 obse...

Asymptotic equivalence for nonparametric regression with multivariate and random design

We show that nonparametric regression is asymptotically equivalent in Le Cam’s sense with a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework based on approximation spaces, which permits to achieve asymptotic equivalence even in the cases of multivariate and random design.

Direct asymptotic equivalence of nonparametric regression and the infinite dimensional location problem

We begin with a random design nonparametric regression having random predictors and Gaussian errors. We produce a convenient, easily implementable mapping of this problem into a Gaussian infinite dimensional location problem. Such an infinite dimensional problem can reflect a Fourier, or wavelet, or other orthogonal basis representation of the original regression situation. In this way it may b...

Asymptotic Equivalence Theory For Nonparametric Regression With Random Noise

ASYMPTOTIC NONEQUIVALENCE OF NONPARAMETRIC EXPERIMENTS WHEN THE SMOOTHNESS INDEX IS 1/2 By

An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric regression, when the smoothness index of the unknown nonparametric function class is 1/2. 1. Introduction. There have recently been several papers demonstrating the global asymptotic equivalence of ce...