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Consistency of a least squares orthonormal series estimator for a regression function

Author

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  • Delecroix, Michel
  • Protopopescu, Camelia

Abstract

This paper establishes the almost. sure consistency of least. squares regression series estimators, in the L2-norm and the sup-norm, under very large assumptions on the underlying model. Three examples are considered in order to illustrate the general results: trigonometric series, Legendre polynomials and wavelet. series estimators. Then optimal choices for the number of functions in the series are discussed and convergence rates are derived. It is shown that. for the wavelet. case, the best. possible convergence rate is attained.

Suggested Citation

  • Delecroix, Michel & Protopopescu, Camelia, 2000. "Consistency of a least squares orthonormal series estimator for a regression function," SFB 373 Discussion Papers 2000,7, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:20007
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    Cited by:

    1. Robert Kast & André Lapied & Sophie Pardo & Camelia Protopopescu, 2001. "Évaluation de risques controversés par la théorie des options réelles," Economie & Prévision, La Documentation Française, vol. 149(3), pages 51-63.
    2. Michel Delecroix & Camelia Protopopescu, 2000. "Are Regression Series Estimators Efficient in Practice? A Computational Comparison Study," Computational Statistics, Springer, vol. 15(4), pages 511-529, December.

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