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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 transfered to local polynomial estimates.

Suggested Citation

  • Birke, Melanie, 2006. "Central limit theorems for the integrated squared error of derivative estimators," Technical Reports 2006,53, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200653
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    File URL: https://www.econstor.eu/bitstream/10419/22697/1/tr53-06.pdf
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    References listed on IDEAS

    as
    1. Birke, Melanie & Dette, Holger, 2006. "Testing strict monotonicity in nonparametric regression," Technical Reports 2006,49, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. 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.
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