Kullback S. — Information theory and statistics :: Электронная библиотека попечительского совета мехмата МГУ

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Kullback S. — Information theory and statistics

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Название: Information theory and statistics

Автор: Kullback S.

Аннотация:

Highly useful text studies the logarithmic measures of information and their application to testing statistical hypotheses. Topics include introduction and definition of measures of information, their relationship to Fisher’s information measure and sufficiency, fundamental inequalities of information theory, much more. Numerous worked examples and problems. References. Glossary. Appendix. 1968 second, revised edition.

Язык:

Рубрика: Computer science/Теория информации/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 399

Добавлена в каталог: 20.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

      5
$N(\mu_{i}, \Sigma_{i})$       189
$R^{n}$       3 386
$T^{-1}(G)$ , definition of      18
$[\lambda]$       4
$\hat{I}(*:2)$       38
$\hat{I}(*:H)$       85
$\sigma$ -algebra      3 386
$\sigma$ -finite measure      386
Absolute continuity      3 29 381
Additive class      3 381
Admissible      39 381
Analysis of covariance      219 239
Analysis of samples      109
Analysis of variance      109
Analysis of variance, multivariate analogue      294
Analysis of variance, multivariate generalization      109
Asymptotic confidence interval      382
Asymptotic distribution      70 97 324 382
Averages, distribution of      191
Averages, distribution of moment generating function of      297
Axiomatic development      12 382
Bartlett, M. S.      302 329
Bartlett’s test for the homogeneity of variances      319
Basis      382
Bayes’ Theorem      4 84
Behrens — Fisher problem      311
Bessel function      327
Best estimate      109 382
Bhattacharyya, A.      41
Bias      382
Biased estimate      58 382
Binary digit      7 382
Bit      7 382
Borel field      3 382
Borel set      3 382
Box, G. E. P.      327
Brownlee, K. A.      188
Canonical correlation      202 204 275 277 279 281
Canonical correlation, discrimination efficiency      278
Canonical correlation, test for      276 278 282
Canonical form      194
Carter, A. H.      229
Categories, grouping      114 116
Centering      217 262
Central limit theorem      101 105
Channel, capacity      9 25
Channel, capacity, noisy      24
Characteristic equation      382
Characteristic function      325 328 329
Characteristic function of a set      21 42 382
Characteristic function, $x^{2}$ -distribution      210 327 330
Characteristic function, noncentral $x^{2}$ -distribution      210 327
Characteristic roots      195
Characteristic vectors      195 382
Chernoff, H.      41 77 86 95 98
Cherry, E. C.      2 3
class      3 382
Classification procedure      85 348
Column effect      239 240
Communication, system      24
Communication, system, theory      1 8 24 382
Comparisons, dichotomous      114 115
Comparisons, dichotomous, pooling      136 147
Complement of one set with respect to another      42 382
Components, principal      197
Concave function      34
Conditional discrimination information      13
Conditional entropy      24
Conditional expectation      19
Conditional homogeneity, analysis of      171 181 184
Conditional homogeneity, null hypothesis of      170
Conditional independence      166 170 182
Conditional information      13
Conditional probability      4 83 117 166
Confidence coefficient      102 382
Confidence interval      91 103 149 382
Confidence interval, binomial      103
Confidence limits      102 382
Confidence region      102
Conjecture      352
Conjugate distribution      81 106 111 143 297 298 310 315 318
Consistent estimate      98 382
Consistent test      100 105
Converge in probability      75 102 382
Converge with probability      1 141 187 382
Convex function      16 34 171
Convex set      98 383
Convexity property      16 114 135 145 157 171
Correlation coefficients, test of homogeneity      321 323
Correlation matrices      192
Correlation matrices, null hypothesis of homogeneity      320
Correlation matrix, null hypothesis specifying      304
Correlation, canonical      200 275 277 279 281
Correlation, canonical, multiple      203
Correlation, canonical, simple      205
Covariance matrices, homogeneity of      315 324
Covariance matrices, test of homogeneity      322
Covariance matrix      189
Covariance matrix of estimates      213 237 255 291
Covariance matrix of linear functions      290
Covariance matrix, null hypothesis specifying      302
Covariance matrix, unbiased sample      192
Covariance variates      204
Covariance, analysis of      219 239
Covariance, multiple      239
Cramer — Rao inequality      36 383
Critical region      74 86
Cumulant generating function      41
Denumerable      383
Determinantal equation      195 197 382
Determinantal equation, roots of      330
Diagonal element      383
Diagonal matrix      192 195
Digit, binary      7 382
Directed divergence      7 82 85
Discriminant function, linear      196 203 205 254 276 305 311 317 342
Discriminant function, sufficient      196
Discrimination efficiency      63 64 65 197 277
Discrimination information      5 19 70 85 196
Discrimination information, conditional      13
Discrimination information, minimum      37 38 81 85 94 109 213 256 302 303
Disjoint sets      383
Distance      6 383
Distance, generalized      190
Distribution, asymptotic      324 382
Distribution, conjugate      81 106 111 143 297 298 310 315 318
Distribution, Fisher’s B      327
Distribution, least informative      111 120 143
Distribution, multivariate normal      189
Distribution, noncentral      257
Distribution, noncentral $x^{2}$       327 328
Distribution, roots of determinantal equation      330
Distribution, Wishart      191 325
Divergence      6 22 41 110 142 190 212 254
Divergence, directed      7 82 85
Dominated set of measures      29 383
Efficiency, discrimination      63 64 65 197 277
Efficiency, estimation      64 65 66
Efficiency, relative      77
Efficient estimate      383
entropy      1 7 34
Entropy, conditional      24
Equivalent measures      383
Equivalent samples      82
Equivalent x’s, sets of      18
Error, type I (II)      74 77 86 125 387
Estimate, consistent      98 382
Estimate, efficient      383
Estimate, maximum-likelihood      94 102

Estimation efficiency      64 65 66
Estimator      81 383
Estimator, unbiased      57 387
Euclidean space      3 383
Event      3 383
Evidence, weight of      5
Expectation, conditional      19
Experiment      10
Experiment, designer of      1
Exponential family      38 84
Exponential type      39 44
Factor analysis      302
Field      383
Finite measure      5 383
Fisher consistent      141
Fisher information matrix      28 49 383
Fisher, R. A.      1 2 13 18 119 141
Fisher’s $B^{2}$ table of      380
Fisher’s B-distribution      327
Fisher’s information      13 26 55
Fisher’s z-test      324
Garner, W. R.      155
Generalized distance      190
Generalized probability density      4 383
Generating function, cumulant      41
Generating function, moment      41 297 385
Gilbert, E. N.      1
Good, I. J.      5 114
Greatest lower bound      383
Green, P. E., Jr      2
Greenhouse, S. W.      344
GT(x), definition of      19
Halmos, P. R.      19
Hartley, R. V. L.      2 7
Homogeneity, conditional      169
Homogeneity, conditional, correlation matrices      320
Homogeneity, conditional, covariance matrices      315 318
Homogeneity, conditional, marginal distributions      179 333
Homogeneity, conditional, means and regressions      272 273
Homogeneity, conditional, means, multivariate samples      264 276 309 311
Homogeneity, conditional, means, single-variate samples      223
Homogeneity, conditional, multinomial samples      128 134 159
Homogeneity, conditional, multivariate normal sample      299
Homogeneity, conditional, normal sample      95
Homogeneity, conditional, null subhypothesis of      225
Homogeneity, conditional, Poisson samples      144
Homogeneity, conditional, regression coefficients      221
Homogeneity, conditional, sample averages      280
Homogeneity, conditional, two-way contingency table      168
Homogeneity, conditional, variances, Bartlett’s test      319
Homogeneous sample, hypothesis about mean of      301
Homogeneous samples      383
Homogeneous set of measures      20 384
Hotelling, H.      199 202 256 268
Hotelling’s      2 213 257 262 279
Hotelling’s canonical correlation coefficients      276
Hotelling’s generalization of Student’s Mest      301
Hyperplane      98 384
Hypotheses, rejection of      3 37 85
Hypotheses, testing      85 109
Hypothesis      384
Hypothesis, conditional      166
Hypothesis, multivariate normal      333
Hypothesis, one-sided      119 121 131 148 151 385
Identity matrix      384
Independence components, analysis of      173
Independence hypotheses      165 182
Independence, conditional      166
Independence, multivariate      303
Independence, sets of variates      276 282 306
Independence, three-way contingency table      160 162 177
Independence, two-way contingency table      156
Indicator of a set      42 384
Inequality, Cramer — Rao      36
Inequality, information      36 55 384
Infimum (inf)      384
Information in a set      16
Information in a variable about another variable      8
Information in a vector about another vector      201
Information in row-categories about (column, depth)-categories      163
Information in row-categories about column categories      156
Information in the elements of a set      16
Information Inequality      36 55 384
Information infinite      6
Information statistic      81 83 85 113 120 124
Information theory      1 2
Information, additivity of      12
Information, bit of      7
Information, Chernoff’s      41
Information, conditional      13
Information, definition of      3 5
Information, discrimination      5 19 70 85 196
Information, experiment      10
Information, Fisher’s      13 26 55
Information, Hartley's      7
Information, logarithmic form of      13
Information, loss of      16 22 74 144
Information, mean      8 142 156 201
Information, pseudo      41
Information, Savage’s      5
Information, selective      7
Information, semantic      2
Information, Shannon’s      2 7 8
Information, transmission of      25
Information, unit of      5 7 8
Information, Wiener’s      2 33
Input space      24
Interaction      171 186 238
Interaction, negative      172 185
Interaction, second-order      188
intersection of two sets      384
Invariance      6
Invariant properties      64 194 292
Inverse image set      18 384
Inverse of a matrix      384
Iteration      343 349
Ito, K.      268
J(1, 2)      6
Jacobian      325 328 384
Jeffreys, H.      6
Jensen’s Inequality      16
Khintchine’s theorem      75 105 384
Klemmer, E.      110
Knowledge, prior      10
Kolodziejczyk, S.      211
Koopman, B. O.      39
Kossack, C. F.      313
Kronecker product of matrices      255 291
Kullback, J. H.      313
Kupperman      83 98
Latin square      238
Lawley, D. N.      256 257 268
Least informative distribution      111 120 143
Least upper bound      71 384
Lehmann, E. L.      93
Levin, S. G.      109
Likelihood ratio      5 94 95 97 104 114 384
Limit inferior (lim inf)      71 384
Limit point      384
Limit superior (lim sup)      384
Lindley, D. V.      9
Linear compound      254 276 278 317 348
Linear discriminant functions, comparison of      351
Linear discriminant functions, minimum error criterion      349
Linear discriminant functions, most divergent      198 200 203 347
Linear discriminant functions, most informative      198 200 203 347
Linear discriminant functions, pair of      204
Linear estimates, minimum variance, unbiased      238 255 292
Linear hypothesis      109 211 212 253
Linear regression model      294

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