## Density Estimation for Statistics and Data AnalysisAlthough 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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### Contents

Survey of existing methods | 7 |

The kernel method for univariate data | 34 |

The kernel method for multivariate data | 75 |

Three important methods | 95 |

Density estimation in action | 120 |

Bibliography | 159 |

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### Common terms and phrases

adaptive kernel algorithm analysis applications approach appropriate approximate assumed asymptotic becomes behaviour bias calculated Chapter choice choose cluster considered constructed context corresponding course cross-validation curve data points data set defined definition density estimate density f density function depends derivative described difficulties direction discriminant discussed distribution equal estimate f example expression formula function further give given histogram idea important integrated square error interest interval kernel estimate kernel method likelihood maximum mean integrated square minimizing Models multivariate natural nearest neighbour nonparametric normal observations obtained Old Faithful geyser original orthogonal series particular penalized likelihood penalty population possible practical present probability density problem procedure projection properties reference roughness rule sample satisfying Section shows Silverman simulation smoothing parameter standard statistical Step substituting suggested Suppose tails technique underlying variable variance various weight window width zero

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