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Density estimation for statistics and data analysis
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London : Chapman and Hall, 1996
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30000003930017 QA276.8 S55 1996 Open Access Book Book

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Although there has been a surge of interest in density estimation in recent years, much of the published research has been concerned with purely technical matters with insufficient emphasis given to the technique's practical value. Furthermore, the subject has been rather inaccessible to the general statistician.

The account presented in this book places emphasis on topics of methodological importance, in the hope that this will facilitate broader practical application of density estimation and also encourage research into relevant theoretical work. The book also provides an introduction to the subject for those with general interests in statistics. The important role of density estimation as a graphical technique is reflected by the inclusion of more than 50 graphs and figures throughout the text.

Several contexts in which density estimation can be used are discussed, including the exploration and presentation of data, nonparametric discriminant analysis, cluster analysis, simulation and the bootstrap, bump hunting, projection pursuit, and the estimation of hazard rates and other quantities that depend on the density. This book includes general survey of methods available for density estimation. The Kernel method, both for univariate and multivariate data, is discussed in detail, with particular emphasis on ways of deciding how much to smooth and on computation aspects. Attention is also given to adaptive methods, which smooth to a greater degree in the tails of the distribution, and to methods based on the idea of penalized likelihood.

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Choice Review

Silverman, in this very interesting book, emphasizes practical applications of density estimation, which he defines as the construction of an estimate of the density function from the observed data. For many years, only purely technical matters were associated with this procedure, and as a result it was generally inaccessible to the average statistician. Silverman has very successfully opened up this difficult area to a wide group of individuals by concentrating on topics of methodological interest. Such topics as nonparametric discriminant analysis, cluster analysis, simulation and the bootstrap, and the estimation of hazard rates provide a context in which density estimation is used. Some representative chapters are ``Existing Methods'' and ``The Kernel Method for Univariate and Multivariate Data,'' with emphasis on how much to smooth. The chapter on density estimation in action is exceptionally well done. Silverman also emphasizes adaptive methods for a greater level of smoothing in the tails of the distribution. A very thorough bibliography as well as a subject and author index. Highly recommended for undergraduate and graduate libraries.-D.J. Gougeon, University of Scranton

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