Abstract
We consider kernel estimates for the derivatives of a probability density which satisfies certain smoothness conditions. We derive the rate of convergence of the local and of the integrated mean square error (MSE and IMSE), by restricting us to kernels with compact support. Optimal kernel functions for estimating the first three derivatives are given. Adopting a technique developed by Farrel (1972) and Wahba (1975), we obtain the optimal rate of convergence of the MSE for non-parametric estimators of derivatives of a density. Kernel estimates attain this optimal rate.
In partial fulfillment of the requirements for the diploma in mathematics (autumn 1978)
Research undertaken within the project "Stochastic mathematical models" at the Sonderforschungsbereich 123, financed by the Deutsche Forschungsgemeinschaft at the University of Heidelberg
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References
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© 1979 Springer-Verlag
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Müller, HG., Gasser, T. (1979). Optimal convergence properties of kernel estimates of derivatives of a density function. In: Gasser, T., Rosenblatt, M. (eds) Smoothing Techniques for Curve Estimation. Lecture Notes in Mathematics, vol 757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098494
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DOI: https://doi.org/10.1007/BFb0098494
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