Combinatorial Methods in Density EstimationSpringer Science & Business Media, 2001年1月12日 - 208 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
II | 1 |
III | 3 |
IV | 4 |
VII | 7 |
IX | 9 |
X | 10 |
XI | 11 |
XII | 13 |
LXXV | 95 |
LXXVI | 98 |
LXXVII | 99 |
LXXVIII | 103 |
LXXIX | 105 |
LXXXI | 107 |
LXXXII | 108 |
LXXXIII | 110 |
XIII | 17 |
XIV | 19 |
XV | 22 |
XVI | 23 |
XVIII | 25 |
XIX | 27 |
XX | 28 |
XXI | 30 |
XXII | 31 |
XXIII | 33 |
XXV | 35 |
XXVI | 38 |
XXVII | 39 |
XXIX | 40 |
XXX | 41 |
XXXII | 42 |
XXXIII | 43 |
XXXVI | 46 |
XXXVII | 47 |
XXXVIII | 49 |
XXXIX | 51 |
XL | 52 |
XLII | 53 |
XLIII | 55 |
XLV | 56 |
XLVII | 57 |
XLVIII | 58 |
XLIX | 60 |
LI | 61 |
LII | 64 |
LIII | 66 |
LV | 68 |
LVI | 70 |
LVII | 71 |
LVIII | 72 |
LIX | 73 |
LX | 74 |
LXI | 76 |
LXIII | 77 |
LXIV | 79 |
LXV | 80 |
LXVI | 81 |
LXVII | 82 |
LXVIII | 83 |
LXIX | 84 |
LXX | 85 |
LXXI | 86 |
LXXII | 88 |
LXXIII | 90 |
LXXXIV | 111 |
LXXXV | 113 |
LXXXVI | 114 |
LXXXVII | 115 |
LXXXIX | 116 |
XC | 118 |
XCI | 121 |
XCII | 122 |
XCIII | 124 |
XCIV | 125 |
XCV | 127 |
XCVII | 132 |
XCVIII | 134 |
XCIX | 135 |
C | 136 |
CI | 138 |
CII | 139 |
CIV | 140 |
CV | 142 |
CVI | 143 |
CVII | 146 |
CVIII | 148 |
CX | 149 |
CXI | 150 |
CXII | 152 |
CXIII | 154 |
CXIV | 156 |
CXV | 159 |
CXVI | 162 |
CXVII | 163 |
CXVIII | 166 |
CXIX | 168 |
CXX | 169 |
CXXI | 174 |
CXXII | 177 |
CXXIV | 179 |
CXXV | 181 |
CXXVI | 184 |
CXXVII | 187 |
CXXVIII | 188 |
CXXX | 190 |
CXXXI | 192 |
CXXXII | 193 |
CXXXIII | 194 |
196 | |
199 | |
203 | |
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常見字詞
Annals of Statistics Asymptotic bandwidth bandwidth h Bibliographic Remarks Birgé Borel sets bounded difference cells Chapter characteristic function Chervonenkis choice class of densities class of sets combinatorial defined denote densi density f Devroye Epanechnikov esti estimate fn example finite fixed func ƒ and g Györfi Hellinger distance histogram Hoeffding's inequality hypercube inequality integrable intervals Jensen's inequality kernel complexity kernel estimate Kh(x Kolmogorov entropy L1 error LEBESGUE DENSITY THEOREM Lipschitz lower bound Lugosi mate minimax minimum distance estimate monotone multivariate nels nonnegative normal density 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 tors transformed uniform unimodal upper bound Vapnik Vapnik-Chervonenkis dimension variable kernel estimates vector Yatracos class zero µn(A АЕА