Silverman B.W. Density Estimation for Statistics and Data Analysis

Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability (Book 26).
— Chapman and Hall/CRC, 1986. — 175 p. — ISBN: 978-0412246203, e-ISBN: 978-1489933249.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.What is density estimation?, Density estimates in the exploration and presentation of data, Further reading.
Survey of existing methods.
Histograms, The naive estimator, The kernel estimator, The nearest neighbour method,
The variable kernel method, Orthogonal series estimators, Maximum penalized likelihood estimators,
General weight function estimators, Bounded domains and directional data, Discussion and bibliography.
The kernel method for univariate data.
Elementary finite sample properties, Approximate properties, Choosing the smoothing parameter,
Computational considerations, A possible bias reduction technique, Asymptotic properties.
Tbe kernel metbod for multivariate data.
The kernel method in several dimensions, Choosing the kernel and the window width, Computational considerations, Difficulties in high-dimensional spaces.
Three important metbods.
The nearest neighbour method, Adaptive kernet estimates, Maximum penalized likelihood estimators.
Density estimation in action.
Nonparametric discriminant analysis, Cluster analysis, Bump hunting and testing for multimodality,
Simulation and the bootstrap, Estimating quantities that depend on the density.