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Biometrika 1987 74(4):743-749; doi:10.1093/biomet/74.4.743
© 1987 by Biometrika Trust
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Bandwidth choice and confidence intervals for derivatives of noisy data

HANS-GEORG MÜLLER, U. STADTMÜLLER and THOMAS SCHMITT

Institut für Medizinisch-Biologische Statistik, Universität Marburg Ernst-Giller-Strasse 20, D-3550 Marburg, Federal Republic of Germany
Abteilung für Mathematik I, Universität Ulm Oberer Eselsberg, D-7900 Ulm, Federal Republic of Germany
Institut für Medizinisch-Biologische Statistik, Universität Marburg Ernst-Giller-Strasse 20, D-3550 Marburg, Federal Republic of Germany

We propose a method for automatic bandwidth selection for kernel estimators of derivatives of a regression function. The finite sample behaviour of this new method is compared with that of other methods in a Monte Carlo Study. The automatic estimation of derivatives can be employed for the construction of asymptotic local confidence intervals for the nonparametric estimate of the regression function and its first derivatives.

Key Words: Bandwidth selection • Cross-validation • Difference quotient • Estimation of derivatives • Factor method • Kernel estimator


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