Combinatorial Methods in Density Estimation
Combinatorial Methods in Density Estimation
ISBN: 9780387951171
出版社: Springer
出版年: 2001-01-12
页数: 220
定价: USD 79.95
装帧: Hardcover
内容简介
Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This book is the first to explore a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric.
作者简介
Gabor Lugosi is Professor at Universitat Pompeu Fabra in Barcelona, and Luc Debroye is Professor at McGill University in Montreal. In 1996, the authors, together with Lászlo Gy?rfi, published the successful text, A Probabilistic Theory of Pattern Recognition with Springer-Verlag. Both authors have made many contributions in the area of nonparametric estimation.
目录
Introduction.- Concentration Inequalities.- Uniform Deviation Inequalities.- Combinatorial Tools.- Total Variation.- Choosing a Density Estimate from a Collection.- Skeleton Estimates.- The Minimum Distance Estimate: Examples.- The Kernel Density Estimate.- Additive Estimates and Data Splitting.- Bandwidth Selection for Kernel Estimates.- Multiparameter Kernel Estimates.- Wavelet Estimates.- The Transformed Kernel Estimate.- Minimax Theory.- Choosing the Kernel Order.- Bandwidth Choice with Superkernels.