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Statistics
A Journal of Theoretical and Applied Statistics
Volume 26, 1995 - Issue 4
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Original Articles

Asymptotic Normality of L1-Error in Density Estimation

Alain Berlinet Université de Montpellier, McGill University, Montreal and Technical University of Budapest,
,
Luc Devroye Université de Montpellier, McGill University, Montreal and Technical University of Budapest,
&
László Györfi Université de Montpellier, McGill University, Montreal and Technical University of Budapest,
Pages 329-343 | Received 15 Nov 1993, Accepted 01 Nov 1994, Published online: 27 Jun 2007

Citations (19)

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Read on this site (6)

László Györfi & Martin Kroll. (2023) Multivariate density estimation from privatised data: universal consistency and minimax rates. Journal of Nonparametric Statistics 35:3, pages 491-513.
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Majid Mojirsheibani & William Pouliot. (2017) Weighted bootstrapped kernel density estimators in two-sample problems. Journal of Nonparametric Statistics 29:1, pages 61-84.
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Majid Mojirsheibani. (2007) Some approximations to L -statistics of kernel density estimators. Statistics 41:3, pages 203-220.
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Jean Geffroy, Stéphane Girard & Pierre Jacob. (2006) Asymptotic normality of the L 1-error of a boundary estimator. Journal of Nonparametric Statistics 18:1, pages 21-31.
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J. Beirlant & L. Gyorfi. (1998) On the lrerror in histogram density estimation: The multidimensional case. Journal of Nonparametric Statistics 9:2, pages 197-216.
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László Györfi, Friedrich Liese, Igor Vajda & Edward C. Van Der Meulen. (1998) Distribution Estimates Consistent in χ2-Divergence. Statistics 32:1, pages 31-57.
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Articles from other publishers (13)

Vaclav Kus & Finger Richard. (2019) Unifying approach to score based statistical inference in physical sciences. Journal of Physics: Conference Series 1391:1, pages 012124.
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Kevin Moon, Kumar Sricharan, Kristjan Greenewald & Alfred HeroIIIIII. (2018) Ensemble Estimation of Information Divergence †. Entropy 20:8, pages 560.
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Bo Liu & Majid Mojirsheibani. (2015) On a weighted bootstrap approximation of the norms of kernel density estimators . Statistics & Probability Letters 105, pages 65-73.
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A. Berlinet. 2014. Wiley StatsRef: Statistics Reference Online. Wiley StatsRef: Statistics Reference Online.
Jorge Silva & Shrikanth Narayanan. (2010) Nonproduct Data-Dependent Partitions for Mutual Information Estimation: Strong Consistency and Applications. IEEE Transactions on Signal Processing 58:7, pages 3497-3511.
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Samuel Kotz, Campbell B. Read, N. Balakrishnan, Brani Vidakovic & Norman L. JohnsonA. Berlinet. 2004. Encyclopedia of Statistical Sciences. Encyclopedia of Statistical Sciences.
Samuel Kotz, Campbell B. Read, N. Balakrishnan, Brani Vidakovic & Norman L. JohnsonA. Berlinet. 2004. Encyclopedia of Statistical Sciences. Encyclopedia of Statistical Sciences.
Stéphane Girard. (2004) On the asymptotic normality of the L1-error for Haar series estimates of Poisson point processes boundaries. Statistics & Probability Letters 66:1, pages 81-90.
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Ferdinand Österreicher & Igor Vajda. (2003) A new class of metric divergences on probability spaces and its applicability in statistics. Annals of the Institute of Statistical Mathematics 55:3, pages 639-653.
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Márta Pintér. (2002) On the rate of convergence of error estimates for the partitioning classification rule. Theoretical Computer Science 284:1, pages 181-196.
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L. Devroye & L. Györfi. 2002. Principles of Nonparametric Learning. Principles of Nonparametric Learning 211 270 .
Alain Berlinet. (1999) How to get Central Limit Theorems for global errors of estimates. Applications of Mathematics 44:2, pages 81-96.
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A. Berlinet, I. Vajda & E.C. van der Meulen. (1998) About the asymptotic accuracy of Barron density estimates. IEEE Transactions on Information Theory 44:3, pages 999-1009.
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