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The Estimation of Nonparametric Functions in a Hilbert Space

Published online by Cambridge University Press:  18 October 2010

A. R. Bergstrom
A. R. Bergstrom*
Affiliation:
University of Essex, England
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Abstract

This paper is concerned with the estimation of a nonlinear regression function which is not assumed to belong to a prespecified parametric family of functions. An orthogonal series estimator is proposed, and Hilbert space methods are used in the derivation of its properties and the proof of several convergence theorems. One of the main objectives of the paper is to provide the theoretical basis for a practical stopping rule which can be used for determining the number of Fourier coefficients to be estimated from a given sample.

Type
Research Article
Information
Econometric Theory , Volume 1 , Issue 1 , April 1985 , pp. 7 - 26
Copyright
Copyright © Cambridge University Press 1985 

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References

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