Bernoulli

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

A continuous Gaussian approximation to a nonparametric regression in two dimensions

Andrew V. Carter

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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.

Article information

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

Dates
First available in Project Euclid: 28 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1141136654

Mathematical Reviews number (MathSciNet)
MR2202326

Zentralblatt MATH identifier
1098.62042

Keywords
asymptotic equivalence of experiments density estimation nonparametric regression

Citation

Carter, Andrew V. A continuous Gaussian approximation to a nonparametric regression in two dimensions. Bernoulli 12 (2006), no. 1, 143--156.https://projecteuclid.org/euclid.bj/1141136654


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