Bernoulli

A continuous Gaussian approximation to a nonparametric regression in two dimensions

Andrew V. Carter

Source: Bernoulli Volume 12, Number 1 (2006), 143-156.

Abstract

Estimating the mean in a nonparametric regression on a two-dimensional regular grid of design points is asymptotically equivalent to estimating the drift of a continuous Gaussian process on the unit square. In particular, we provide a construction of a Brownian sheet process with a drift that is almost the mean function in the nonparametric regression. This can be used to apply estimation or testing procedures from the continuous process to the regression experiment as in Le~Cam's theory of equivalent experiments. Our result is motivated by first looking at the amount of information lost in binning the data in a density estimation problem.

Keywords: asymptotic equivalence of experiments; density estimation; nonparametric regression

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.bj/1141136654
Mathematical Reviews number (MathSciNet): MR2202326
Zentralblatt MATH identifier: 1098.62042

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