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Asymptotics for Lp-norms of Fourier series density estimators

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Abstract

LetX 1, X2, ⋯, be a sequence of independent, identically distributed bounded random variables with a smooth density functionf. We prove that\(\int_a^b | f_{m,n} (t) - f(t)|^p w(t)dt(1 \leqslant p< \infty )\) is asymptotically normal, wheref m, n is the Fourier series density estimator offandw is a nonnegative weight function.

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Authors and Affiliations

  1. Bolyai Institute, Szeged University, Aradi vértanúk tere 1, H-6720, Szeged, Hungary

    Lajos Horváth

  2. Department of Mathematics, University of Utah, 84112, Salt Lake City, Utah, USA

    Lajos Horváth

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  1. Lajos Horváth
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Additional information

Communicated by Edward B. Saff.AMS classification: Primary 60F05, 60F25; Secondary 62G05.

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Horváth, L. Asymptotics for Lp-norms of Fourier series density estimators. Constr. Approx 6, 375–397 (1990). https://doi.org/10.1007/BF01888271

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  • DOI: https://doi.org/10.1007/BF01888271

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