RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 4, Pages 674–690 (Mi tvp19)

An exponential estimate for a wavelet density estimator

J. Gama, V. V. Yurinskii

University of Beira Interior

Abstract: This article is dedicated to deriving an exponential inequality for the distribution of the $L^p$-norm of the discrepancy between a one-dimensional probability density and its wavelet estimator that uses thresholding. In the underlying multiresolution analysis, the scale function and the mother wavelet are supposed to have compact support. The exponential estimate obtained is akin to Bernstein's inequality for sums of independent random variables. It supplements the known bounds for the mean integrated risks. The proof exploits the near-independence of empirical approximations to the coefficients of the same multiresolution level that correspond to wavelets with well-separated supports.

DOI: https://doi.org/10.4213/tvp19

Full text: PDF file (1528 kB)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2007, 51:4, 595–608

Bibliographic databases:

Citation: J. Gama, V. V. Yurinskii, “An exponential estimate for a wavelet density estimator”, Teor. Veroyatnost. i Primenen., 51:4 (2006), 674–690; Theory Probab. Appl., 51:4 (2007), 595–608

Citation in format AMSBIB
\Bibitem{GamYur06} \by J.~Gama, V.~V.~Yurinskii \paper An exponential estimate for a~wavelet density estimator \jour Teor. Veroyatnost. i Primenen. \yr 2006 \vol 51 \issue 4 \pages 674--690 \mathnet{http://mi.mathnet.ru/tvp19} \crossref{https://doi.org/10.4213/tvp19} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2338061} \zmath{https://zbmath.org/?q=an:1127.62031} \elib{http://elibrary.ru/item.asp?id=9310056} \transl \jour Theory Probab. Appl. \yr 2007 \vol 51 \issue 4 \pages 595--608 \crossref{https://doi.org/10.1137/S0040585X97982657} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000251875600002} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38149118996}