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The Estimation of Nonparametric Functions in a Hilbert Space

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  • Bergstrom, A. R.

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.

Suggested Citation

  • Bergstrom, A. R., 1985. "The Estimation of Nonparametric Functions in a Hilbert Space," Econometric Theory, Cambridge University Press, vol. 1(1), pages 7-26, April.
    • Handle: RePEc:cup:etheor:v:1:y:1985:i:01:p:7-26_01
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    Cited by:

    1. Jun Yu, 2009. "Econometric Analysis of Continuous Time Models : A Survey of Peter Phillips’ Work and Some New Results," Microeconomics Working Papers 23046, East Asian Bureau of Economic Research.
    2. Yu, Jun, 2014. "Econometric Analysis Of Continuous Time Models: A Survey Of Peter Phillips’S Work And Some New Results," Econometric Theory, Cambridge University Press, vol. 30(4), pages 737-774, August.

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