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Nonparametric polynomial density estimation in the L P norm

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Approximation and Optimization

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1354))

Abstract

A simple construction of polynomial estimators for densities and distributions on the unit interval is presented. For densities from certain Lipschitz classes the error for the mean Lp deviation is characterised. The Casteljeau algorithm for calculating the values of the estimators is applied.

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References

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Authors and Affiliations

  1. Instytut Matematyczny PAN, ul. Abrahama 18, 81-825, Sopot, Poland

    Z. Ciesielski

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  1. Z. Ciesielski
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Editor information

Juan Alfredo Gómez-Fernandez Francisco Guerra-Vázquez Guillermo López-Lagomasino Miguel A. Jiménez-Pozo

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© 1988 Springer-Verlag

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Ciesielski, Z. (1988). Nonparametric polynomial density estimation in the L P norm. In: Gómez-Fernandez, J.A., Guerra-Vázquez, F., López-Lagomasino, G., Jiménez-Pozo, M.A. (eds) Approximation and Optimization. Lecture Notes in Mathematics, vol 1354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089579

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  • DOI: https://doi.org/10.1007/BFb0089579

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50443-6

  • Online ISBN: 978-3-540-46005-3

  • eBook Packages: Springer Book Archive

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