Density Estimation for Statistics and Data Analysis
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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Survey of existing methods
The kernel method for univariate data
The kernel method for multivariate data
Three important methods
Density estimation in action
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adaptive kernel estimate adaptive kernel method algorithm approach approximate asymptotic bandwidth behaviour bias bimodal bivariate bumps choice of smoothing choosing the smoothing cluster analysis considered context data points data set defined density estimate constructed density f depends discussed in Section Epanechnikov estimate f example fast Fourier transform Fourier transform give given in Fig grid herit histogram integrated square error interval kernel density estimate least-squares cross-validation likelihood cross-validation log likelihood maximum penalized likelihood mean integrated square mean square error minimizing multivariate naive estimator nearest neighbour estimate nearest neighbour method normal density normal distribution normal kernel observations obtained Old Faithful geyser orthogonal series pilot estimate population probability density function problem projection pursuit properties roughness penalty sample X1 Silverman 1978a simulation smoothed bootstrap smoothing parameter ſº standard statistical tails test graph true density unimodal univariate unknown density variable kernel variance weight function width h window width zero