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Central limit theorems for the integrated squared error of derivative estimators

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  • Birke, Melanie

Abstract

A central limit theorem for the weighted integrated squared error of kernel-type estimators of the first two derivatives of a nonparametric regression function is proved by using results for martingale differences and U-statistics. The results focus on the setting of the Nadaraya-Watson estimator but can also be transferred to local polynomial estimates.

Suggested Citation

  • Birke, Melanie, 2008. "Central limit theorems for the integrated squared error of derivative estimators," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1903-1913, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:13:p:1903-1913
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    References listed on IDEAS

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    1. Ioannides, Dimitrios A., 1992. "Integrated square error of nonparametric estimators of regression function: the fixed design case," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 85-94, September.
    2. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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    Cited by:

    1. Melanie Birke & Holger Dette & Kristin Stahljans, 2011. "Testing symmetry of a nonparametric bivariate regression function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 547-565.

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