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## Details

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:

## Reviews

*Editorial reviews*

Publisher Synopsis

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 papers of the two authors in the Annals of Statistics. It is based on ideas of minimum distance methods and convergence theory for empirical measures, uniformly over certain classes. The methods aim at finding estimators with universal properties that is valid for all (or nearly all) densities. The book is self-contained because a lot of fundamental inequalities and essential combinatorial techniques are collected in the first part of the book. There is a rich choice of exercises, some of which may be quite hard. This makes it interesting for classroom teaching. It is an attractive book that certainly provides inspiration for further research."Short Book Reviews, Vol. 21, No. 2, August 2001"The book deals with probability density estimation from an i.i.d. sample, but the approach is different from those used in other texts on this topic. ... It is the aim of the book to study universal performance properties of these estimates. ... it is well written following the same idea throughout and contains many exercises which complete the different topics. ... I enjoyed reading this nicely written book which can certainly be recommended to all mathematically orientated statisticians interested in the subject." (Ulrich Stadtmuller, Mathematical Reviews, Issue 2002 h)"This carefully written monograph focuses on nonparametric estimation of a density from i.i.d. data, with the goodness-of-fit being measured in terms of the L1-norm. ... The book is recommended to those who want to get an overview of the state of the art of this approach." (W. Stute, Zentralblatt MATH, Vol. 964, 2001) Read more...

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