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Combinatorial Methods in Density Estimation

Author: Luc Devroye; Gábor Lugosi
Publisher: New York, NY : Springer New York, 2001.
Series: Springer series in statistics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This text explores a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Luc Devroye; Gábor Lugosi
ISBN: 9781461301257 1461301254
OCLC Number: 852792053
Description: 1 online resource (xii, 208 pages).
Contents: Introduction --
Concentration Inequalities --
Uniform Deviation Inequalities --
Combinatorial Tools --
Total Variation --
Choosing a Density Estimate from a Collection --
Skeleton Estimates --
The Minimum Distance Estimate: Examples --
The Kernel Density Estimate --
Additive Estimates and Data Splitting --
Bandwidth Selection for Kernel Estimates --
Multiparameter Kernel Estimates --
Wavelet Estimates --
The Transformed Kernel Estimate --
Minimax Theory --
Choosing the Kernel Order --
Bandwidth Choice with Superkernels.
Series Title: Springer series in statistics.
Responsibility: by Luc Devroye, Gábor Lugosi.

Abstract:

Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths.  Read more...

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From the reviews of the first edition:"This book is built around a new look on the important problem of bandwidth selection in density estimation. This new method has been launched in two recent Read more...

 
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   schema:description "Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This text explores a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric. It is the first book on this topic. The text is intended for first-year graduate students in statistics and learning theory, and offers a host of opportunities for further research and thesis topics. Each chapter corresponds roughly to one lecture, and is supplemented with many classroom exercises. A one year course in probability theory at the level of Feller's Volume 1 should be more than adequate preparation. Gabor Lugosi is Professor at Universitat Pompeu Fabra in Barcelona, and Luc Debroye is Professor at McGill University in Montreal. In 1996, the authors, together with Lászlo Györfi, published the successful text, A Probabilistic Theory of Pattern Recognition with Springer-Verlag. Both authors have made many contributions in the area of nonparametric estimation."@en ;
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