Density Estimation for Statistics and Data Analysis

Monographs on Statistics and Applied Probability #26

by Bernard W. Silverman

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.

186 pages, Hardcover

First published April 1, 1986

About the author

Sir Bernard Walter Silverman is a British statistician and former Anglican clergyman.


Source:
Wikipedia

Reviews

[Kostiantyn Shevchenko · Rating 5 out of 5]

At university we were all taught the histogram method for estimating a probability density. This book is an introductory text describing a family of more advanced methods that scale much better in higher dimensions. Early chapters already contain introductory information about what is referred to in current machine learning literature in regard to hyperparameter tuning as Parzen window estimators.

[Sandra Delgado · Rating 4 out of 5]

Buenos ejemplos y bien explicado.

[Do Tuan Hoang · Rating 4 out of 5]

Quyển này giới thiệu một số phương pháp density estimate và tập trung vào KDE. Ngắn gọn, mạch lạc và phần toán thì giải thích các thứ chi tiết đến mức như mình còn hiểu được! Highly recommended!