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

Linear regression, common      268
Linear regression, k categories      219
Linear regression, test of      214
Linear regression, two-way classification      239
Linear set      385
Linear transformation      385
Linear transformation, nonsingular      194 385
Linearly independent functions      385
Linearly independent vectors      385
Log n, tables of      109 110 367
Lower bound      75 385
MacDonald, D. K. C.      8
Mahalanobis, P. C.      190
Mann, H. B.      102
Marginal distributions, homogeneity of      179 333
Matrices      189
Matrices, direct product of      255 291 293
Matrices, inverse of direct product of      256 292
Matrix      385
Matrix differentiation      298
Matrix factorization      302
Matrix inequality      56 292
Matrix, diagonal      192 195
Matrix, nonsingular      385
Matrix, orthogonal      199 386
Matrix, positive      237 289 386
Matrix, positive definite      386
Matrix, rank of      386
Maximum likelihood      85 94
Maximum likelihood, equations      118 139 176
Maximum likelihood, estimate      94 102
McCall, C. H., Jr      238
McGill, W. J.      155
Means, homogeneity of      223 264 272 273 276 309 311
Measurable function      4 385
Measurable set      1 3 385
Measurable space      3 385
Measurable statistic      18
Measurable transformation      18 70 385
Measure      385
Measure, $\sigma$ -finite      386
Measure, probability      3 386
Minor      56 385
Minor, principal      386
Modulo $\lambda$       4
Moment generating function      41 297 385
Most powerful test      385
Mourier, E.      77
Multinomial distribution, conditional      116
Multinomial distribution, conditional, fitting      117 139
Multinomial populations, tests of      112
Multiple correlation      203
Multiple covariance      239
Multivalued population      155
Multivariate normal density      189
Multivariate regression, test of      264
N log n, tables of      109 110 367
Neighborhood of a point      385
Neyman criterion, sufficient statistic      45
Neyman's $x^{2}$       2 114
Neyman, J.      87 94 114
Nit      8
Noise power      9
Noncentral $x^{2}$       5 106 127 210 257
Noncentral $x^{2}$ , distribution      327 328
Noncentral $x^{2}$ , table of      380
Noncentral distributions      257
Noncentrality parameter      105 106 125 146 158 162 165 210 257 327
Nonsingular linear transformation      385
Nonsingular matrix      385
Nonsingular transformation      21 385
Normal density      8 14 189
Normal equations      212 215 216 220 221 226 230 237 255 258 289
Notation, matrix      189
Notation, under various hypotheses      220
Observations, definitive      4
Observations, grouping of      16 22
Observations, missing      238
Observations, probabilistic      1
Observations, raw      219 231 234 260
Observations, statistical      3 15
Odds, posterior      5
Odds, prior      5
Okano, F.      234
One-sided hypothesis      119 121 131 148 151 385
One-to-one transformation      385
Open set      386
Orthogonal matrix      199 386
Output space      24
Parameter matrix      220 254
Parameter matrix, partitioning of      214 294
Parameter matrix, sufficient estimate of      293
Parameter matrix, unbiased estimate of      289
Parameter space      98 386
Partial correlation      210
Partitioning of samples      138
Partitioning of tables      173
Partitioning, sufficient      18
Pearson, E. S.      87 94 322
Pearson, K.      8
Pearson’s x      2 114
Pierce, J. R.      1
Pillai, K. C. S.      257
Pitman, E. J. G.      39
Point      386
Point function      386
Pooling, of samples      147 188
Positive definite      14
Positive definite, matrix      386
Positive definite, quadratic form      386
Positive matrix      237 289 386
Positive quadratic form      386
Power, noise      9
Power, noise of a test      386
Power, noise, signal      9
Powers, K. H.      2 13 33
Principal components      199
Principal direction      64
Principal minor      386
Probability density, generalized      4 383
Probability measure      3 386
Probability space      3 386
Probability, conditional      4 24 83
Probability, conditional, posterior      5

Probability, conditional, prior      5
Probability, conditional, theory of      1
Quadratic form      56 386
Quadratic form, positive      386
Quadratic form, positive definite      386
Radon — Nikodym, derivative      4 29
Random variable      386
Rank of a matrix      386
Rate of transmission      24 25
Region of acceptance (rejection)      74 386
Regression model      294
Regression model, Carter's      229
Regression model, k-category      221 222 225
Regression model, multivariate      253 254 258 265 269
Regression, null hypothesis of no      269
Regression, test of      268 273
Regression, test of subhypothesis      282 286 287
Regression, two-way classification, analysis of      239
Regularity conditions      26 98
Relation, measure of      8 9 25 156 160 163 199 201
Reparametrization      238 289
Replication      238
Rippe, D. D.      302
Roberts, H. R.      103
Rosenblatt, H.      234
Rothstein, J.      1
Row effect      239 240
Sakaguchi      77
Sample averages, moment generating function of      297
Sample space      3
Sample unbiased covariance matrix, moment generating function of      297
Samples, equivalent      82
Samples, equivalent, multivariate normal      191
Sampling theorem      9
Savage, L. J.      2 3 5 19 36
Scale factor in $x^{2}$ approximation      328
Schuetzenberger M. P.      41
Semantic information      2
Sequential analysis      2 43
Set      3 386
Set function      386
Set of measures, dominated      29
Set of measures, homogeneous      20
Shannon's information      2 7 8
Shannon, C. E.      1 2 24 25 37
Signal power      9
Size (of a test)      387
Smith, C. A. B.      321 344 348
Space      387
Space, Euclidean      3 383
Space, input      24
Space, measurable      3 385
Space, output      24
Space, parameter      98 386
Space, probability      3 386
Space, sample      3
Specified mean, test of      300
Statistic      18 70 387
Statistic, sufficient      18 20 21 22 24 44 59
Statistics, mathematical      1
Stein, C.      77
Stirling’s approximation      326
Stuart, A.      334
Stuart’s test      333
Student’s t-test      97 301
Stumpers, F. L. H.      1 2
Subhypothesis      214 258
Subhypothesis, test of      216 260
Sufficiency, criterion of      18 45
Sufficient partitioning      18
Sufficient statistic      18 20 21 22 24 44 59
Supremum (sup)      387
Symmetry, null hypothesis of      177 178
Symmetry, test for      179
Table, contingency      155
Table, contingency, Fisher's $B^{2}$       380
Table, contingency, log tt      109 110 367
Table, contingency, n log n      109 110 367
Table, contingency, noncentral $x^{2}$       380
Tensor, fundamental      64
Test, consistent      100 105
Test, consistent, most powerful      385
Test, consistent, power of      386
Test, consistent, size of      387
Test, consistent, uniformly most powerful      387
Theorem      29 386
Theory      387
Theory, communication      1 24 382
Theory, information      1 2
Three-partition subhypothesis, test of      288
Trace      387
Transformation      18 22 387
Transformation, Jacobian of      325 328 384
Transformation, linear      385
Transformation, matrix      387
Transformation, nonsingular      21 385
Transformation, one-to-one      385
TRANSPOSE      387
Truncation      15 22 387
Tuller, W. G.      1 7
Two-way table with no regression      250
Two-way tables, homogeneity of      168
Type I (II) error      74 77 86 125 387
Unbiased estimator      57 387
Uncertainty      4 7 17 155
Uncertainty, posterior      24
Uncertainty, prior      24
Uniformly most powerful test      387
Union of two or more sets      387
Upper bound      387
Variance, unbiased      50
Variances, Bartlett's test for homogeneity of      319
Variances, independence and equality of      307
Variates, covariance      204
Vector      189 387
Wald, A.      2 74 98 102
Wiener's information      2 33
Wiener, N.      1 2
Wilks' theorem      98
Wilks, S. S.      97 114 322
Wishart distribution      191 325
Wishart distribution, reproductive property      325
Woodward, P.M.      2
“Resemblance      37 82

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