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February 2006 A continuous Gaussian approximation to a nonparametric regression in two dimensions
Andrew V. Carter
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Bernoulli 12(1): 143-156 (February 2006).

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.

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Andrew V. Carter. "A continuous Gaussian approximation to a nonparametric regression in two dimensions." Bernoulli 12 (1) 143 - 156, February 2006.

Information

Published: February 2006
First available in Project Euclid: 28 February 2006

zbMATH: 1098.62042
MathSciNet: MR2202326

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability

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Vol.12 • No. 1 • February 2006
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