Asymptotic equivalence for nonparametric regression with multivariate and random design

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.

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 experiments with random design

where ζi ∼ N (0, 1), and the Xi are marginally i.i.d. with density g on [0, 1]. This nonparametric regression problem with random design is a more realistic model than assuming the data will be observed on a regular grid. How much of a difference does it make whether the Xi are randomly placed given that we have a sufficiently large number of observations? Our approach will be to find a statist...

Asymptotic Equivalence Theory For Nonparametric Regression With Random Noise

Asymptotic Equivalence for Nonparametric Regression

We consider a nonparametric model E, generated by independent observations Xi, i = 1, ..., n, with densities p(x, θi), i = 1, ..., n, the parameters of which θi = f(i/n) ∈ Θ are driven by the values of an unknown function f : [0, 1]→ Θ in a smoothness class. The main result of the paper is that, under regularity assumptions, this model can be approximated, in the sense of the Le Cam deficiency ...