Combinatorial Methods in Density EstimationSpringer Science & Business Media, 2012年12月6日 - 209 頁 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 text explores 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. It is the first book on this topic. The text is intended for first-year graduate students in statistics and learning theory, and offers a host of opportunities for further research and thesis topics. Each chapter corresponds roughly to one lecture, and is supplemented with many classroom exercises. A one year course in probability theory at the level of Feller's Volume 1 should be more than adequate preparation. 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 Györfi, 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. |
內容
1 | |
Uniform Deviation Inequalities | 17 |
Combinatorial Tools | 27 |
Total Variation | 38 |
Choosing a Density Estimate | 47 |
Skeleton Estimates | 58 |
Examples | 70 |
The Kernel Density Estimate | 79 |
Bandwidth Selection for Kernel Estimates | 108 |
Multiparameter Kernel Estimates | 118 |
Wavelet Estimates | 134 |
The Transformed Kernel Estimate | 142 |
Minimax Theory | 150 |
Choosing the Kernel Order | 177 |
Bandwidth Choice with Superkernels | 190 |
199 | |
其他版本 - 查看全部
常見字詞
Annals of Statistics asymptotic bandwidth h Birgé Borel sets bounded difference cells chapter characteristic function Chervonenkis choice class of densities class of sets combinatorial defined denote densi densities ƒ density estimate Devroye Epanechnikov esti estimate fn example finite fixed fn(x func ƒ and g Györfi Hellinger distance histogram Hoeffding's inequality hypercube inequality integrable intervals Jensen's inequality kernel complexity kernel density kernel estimate Kolmogorov entropy L1 error LEBESGUE DENSITY THEOREM Lipschitz lower bound Lugosi mate minimax minimum distance estimate monotone multivariate nels nonnegative nonparametric normal density Note number of different obtain optimal parameter partition polynomial probability random variables rate of convergence real line Riemann Scheffé Section selection shatter coefficient Show Talagrand Theory timate tion transformed uniform unimodal upper bound Vapnik Vapnik-Chervonenkis dimension variable kernel estimate vector Yatracos class zero