The Estimation of Nonparametric Functions in a Hilbert Space
- 1 April 1985
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 1 (1) , 7-26
- https://doi.org/10.1017/s0266466600010975
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.Keywords
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