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Are Regression Series Estimators Efficient in Practice? A Computational Comparison Study

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  • Michel Delecroix

    (CREST-ENSAI)

  • Camelia Protopopescu

    (Centre de la Vieille Charité)

Abstract

Summary This paper is concerned with the practical performances of series-type estimators of a regression function. For different choices of orthonormal bases (Legendre polynomials, trigonometric functions, wavelets) we compare, by simulation arguments, the performances of series-type estimators with the results obtained by two of the most popular nonparametric regression estimation methods: kernel estimation and least-squares cubic splines. It will be shown that orthonormal series estimators are competitive in relation to these former nonparametric procedures. No agreement has emerged on the best method, the results being highly dependent on the nature of the estimated regression function.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:15:y:2000:i:4:d:10.1007_s001800000045
    DOI: 10.1007/s001800000045
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    References listed on IDEAS

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    1. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, March.
    2. 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.
    3. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    4. Antoniadis, Anestis & Dinh Tuan Pham, 1998. "Wavelet regression for random or irregular design," Computational Statistics & Data Analysis, Elsevier, vol. 28(4), pages 353-369, October.
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    Cited by:

    1. Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2014. "Testing for additivity in partially linear regression with possibly missing responses," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 51-61.

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