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| Авторизация |
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| Rao R.C. — Linear Statistical Inference and Its Applications |
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| Предметный указатель |
Estimation, Hellinger distance 352
Estimation, inadmissibility of sample mean (Stein) 343
Estimation, information limit to variance (Cramer, Rao) 324—326
Estimation, information matrix 331
Estimation, information measure 329—331
Estimation, Kullback — Leibler separator 352
Estimation, law of equal ignorance 336
Estimation, law of succession 336
Estimation, least squares See Linear estimation Gauss
Estimation, maximum likelihood See Maximum likelihood
Estimation, method of moments 351
Estimation, method of scoring 367—370
Estimation, minimax 341
Estimation, minimum chi-square 352
Estimation, minimum variance 317—329
Estimation, pooling of estimators 389
Estimation, sufficient statistic See Sufficiency
Estimation, СUAN estimator 350
Expectation, conditional (given statistic) 96
Expectation, conditional (given subfield) 141
Expectation, conditional (substitution in) 153
Expectation, definition and theorems 92
Expectation, moments 93
Exponential family of distributions 195
F (central), Fisher 167
Factor analysis 587
Factorial moments 102
Feller, W. 79 153
Ferguson, T.S. 139 153
Fiducial probability 339
Finney, D.J. 373 380
Fisher's F 167
Fisher's z 167
Fisher, R.A. 44 78 167 174 286 312 313 324 329 339 345 348 351 373 380 428 438 442 444 463 502 504 505 513 542 556 566 568 599 602
Fisz, M. 518 603
Focke, J. 304 312
Fortet, R. 154
Fraser — Sprott equation 207
Fraser, D.A.S. 207 340 380 510 513
Frechet, M. 518 602
G-inverse See Matrix inversion
Gantmacher, F.R. 44 45 46 78
Gart, J.J. 324 380
Gauss — Markoff theory (multivariate), additional information (test for) 551
Gauss — Markoff theory (multivariate), analysis of dispersion See Analysis of dispersion
Gauss — Markoff theory (multivariate), BLIMBE (best linear minimum bias) 306
Gauss — Markoff theory (multivariate), BLUE (best linear unbiased), correlated observations 229
Gauss — Markoff theory (multivariate), BLUE (best linear unbiased), efficiency of estimators 233
Gauss — Markoff theory (multivariate), BLUE (best linear unbiased), geometric solution 228
Gauss — Markoff theory (multivariate), BLUE (best linear unbiased), least squares theory 223
Gauss — Markoff theory (multivariate), BLUE (best linear unbiased), normal equations 222 230
Gauss — Markoff theory (multivariate), BLUE (best linear unbiased), random parameters 234
Gauss — Markoff theory (multivariate), BLUE (best linear unbiased), simultaneous confidence intervals 240
Gauss — Markoff theory (multivariate), BLUE (best linear unbiased), simultaneous estimation 233
Gauss — Markoff theory (multivariate), BLUE (best linear unbiased), singular covariance for observations See Linear estimation-Unified theory
Gauss — Markoff theory (multivariate), choice of design matrix 235
Gauss — Markoff theory (multivariate), covariance analysis 552
Gauss — Markoff theory (multivariate), estimation (BLUE etc.) 544—547
Gauss — Markoff theory (multivariate), Gauss — Markoff model 221
Gauss — Markoff theory (multivariate), growth model 561
Gauss — Markoff theory (multivariate), model (general) 543 544
Gauss — Markoff theory (multivariate), random parameters 234
Gauss — Markoff theory (multivariate), restricted parameters 231
Gauss — Markoff theory (multivariate), structural relationship (dimensionality) 556 564
Gauss — Markoff theory (multivariate), tests of hypotheses 237—240
Gauss — Markoff theory (multivariate), tests of linear hypotheses 547—551
Gauss — Markoff theory (multivariate), variance of estimator 226 230
Gauss — Markoff theory (univariate), BLE (best linear) 305
Gauss, K.F. 220 312
Gauss-Markoff theory (multivariate), applications 562—573
Gayen, A.K. 432 442
Ghosh, J.K. 132 379
Ghosh, Malay 599
Gihman, I.I. 422 442
Girshick, M.A. 497 512 542 602
Glivenko, V.I. 421 442
Gnanadesikan, R. 573 603
Gnedenko, B. V. 79 128 154
Godambe, V.P. 355 377 380 381 513
Goldman, A.J. 220 312
Gram — Schmidt orthogonalization 10
Graybill, F.A. 189 218 252 313
Grenander, U. 79 154 518 602
Growth model (Pothoff, Roy) 561
Guttman, L. 72 78
Hajek, J. 143 154
Haldane, J.B.S. 352 366 381 511 513
Halmos, P.R. 4 78 84 137 154
Hamburger, H. 106 154
Hartley, H.O. 313
Healy, M.J.R. 579 601
Heyde, С.С. 152
Hodges, J.L., Jr. 324 347 381 470 513
Hoeffding, W. 70 504 513
Hoerl, A.E. 306 312
Hogben, L. 444 513
Hogg, R.V. 189 218
Hooke, B.G.E. 272 280 313
Hotelling's  542
Hotelling's  (non-null) 542
Hotelling, H. 542 582 602
Householder, A.S. 21 75 78 231
Hsu, P.L. 228 313 542 602
Huzurbazar's conjecture (sufficiency) 132
Huzurbazar, V.S. 366 381
Hypothesis See Testing of hypotheses
Identification problem 491
Independence of events 90
Inequalities (algebraic), Bessel 10
Inequalities (algebraic), Cauchy — Schwarz 54
Inequalities (algebraic), Frobenius 31
Inequalities (algebraic), Hadamard 56
Inequalities (algebraic), Hoelder 55
Inequalities (algebraic), information theory 58
Inequalities (algebraic), Jensen 58
Inequalities (algebraic), Kantorovich 74
Inequalities (algebraic), Lagrange identity 55
Inequalities (algebraic), Minkowski 56
Inequalities (algebraic), moments 56
Inequalities (algebraic), Sylvester's law 31
Inequalities (Probability), Berge 145
Inequalities (Probability), Camp — Meidell 145
Inequalities (Probability), Cantelli 145
Inequalities (Probability), Chebyschev 95
Inequalities (Probability), Chebyschev type 145
Inequalities (Probability), Hajek — Renyi 114 143
Inequalities (Probability), Hoelder 149
Inequalities (Probability), Jensen 149
Inequalities (Probability), Kolmogorov 143
Inequalities (Probability), Minkowski 149
Inequalities (Probability), Peek 145
Infinitely divisible distribution 149
Information limit to variance (Cramer, Rao) 324—326
Information measure (Fisher) 329—331
Intrinsic accuracy (Fisher) 331
Invariance, principle for CLT 148
Invariance, principle in estimation 343
Invariance, probability measures 138
Invariance, statistical procedure 139
James, А.Т. 542 602
Jeffreys, G.M. 154 336 381 444 513
Jenkins, G.M. 444 505 512
John, S. 579 603
Joos, George 174 218
Kac, M. 147 154
Kagan, A. 79 218 379 527
Kallianpur, G. 347
Katti, S.K. 322 380
Kempthorne, O. 286 287 313 504 513
Kennard, R.W. 306 312
| Khatri, С.G. 29 30 78 165 527 528 543 603
Kiefer, J. 363 381 425 442
Kinchin, A.Ya. 112 146
Kolmogorov, A.N. 79 83 98 128 146 153 322 381 421
Krishnaih, P.R. 543
Kshirsagar, A.M. 593 603
Kyburgh, H.E., Jr. 44 514
Law (zero or one) 148
Law of equal ignorance 336
Law of iterated logarithms 129 130 488
Law of large numbers, Chebychev's theorem (WLLN) 112
Law of large numbers, definition (WLLN, SLLN) 112
Law of large numbers, Kinchin's theorem (WLLN) 112 146
Law of large numbers, Kolmogorov (SLLN) 114 115
Law of large numbers, Kolmogorov (WLLN) 146
Law of large numbers, other theorems 146
Law of succession 336
Lawley.D.V. 587 603
Least squares See Gauss — Markoff Linear
Lebegue integral 133 134
Lebegue — Stieltjes integral 132
LeCam, L. 347 366 381
Lehmann, E.L. 141 153 322 324 381 411 442 463 470 501 513 514
Lemmas named after authors, Borel — Cantelli 137
Lemmas named after authors, Farka 53
Lemmas named after authors, Fatou 135
Lemmas named after authors, Helly 117
Lemmas named after authors, Kronecker 148
Lemmas named after authors, Neyman — Pearson 446
Lemmas named after authors, Schur 77
Levi, F.W. 22 78
Levy, P. 79 154
Likelihood 353
Likelihood ratio (monotone) 461
Likelihood ratio test (Neyman — Pearson) 417
Limit theorems See Central limit theorems Law Distributions Convergence
Lindley, D.V. 444 512 514
Linear equations 6
Linear estimation (Unified theory), basic lemma on g-inverse 294
Linear estimation (Unified theory), Gauss — Markoff model See Gauss — Markoff theory
Linear estimation (Unified theory), general Gauss — Markoff model 297
Linear estimation (Unified theory), I. P. M. method 298
Linear estimation (Unified theory), test for consistency 297
Linear estimation (Unified theory), test of linear hypotheses 299
Linear estimation (Unified theory), U. L. S. method 300
Linear estimation (Unified theory), variances and covariances 298 301
Linnik, Yu., V. 79 154 218 219 286 313 379 463 464 514 527
Lipton, S. 579 601
Loeve, M. 79 86 129 130 147 154
Mahalanobis  542
Mahalanobis, P.C. 474 514 595 597
Mann, H.В. 124 154
Mardia, К.V. 178
Markoff, A.A. 220 313
Martin, F.В. 220 313
Mathai, A.M. 543
Matrix circulant 68
Matrix derivatives 71 72
Matrix inversion, computation of g-inverse 27 34 224
Matrix inversion, duality between  and  49
Matrix inversion, g-inverse 24
Matrix inversion, least squares inverse 48
Matrix inversion, left inverse 16
Matrix inversion, minimum norm inverse 48
Matrix inversion, minimum norm least squares inverse 49
Matrix inversion, Moore — Penrose inverse 26 49
Matrix inversion, reflexive g-in verse 26
Matrix inversion, right inverse 16
Matrix null space 27 31
Matrix nullity 27
Matrix product, Hadamard 30
Matrix product, Kronecker 29
Matrix product, new product (Khatri — Rao) 30
Matrix range space 27
Matrix rank 16
Matrix reduction, commuting matrices 41
Matrix reduction, diagonal form 19 20
Matrix reduction, echolon form 18
Matrix reduction, Frobenius theorem 46
Matrix reduction, Hermite canonical form 18
Matrix reduction, Hermitian matrix 42
Matrix reduction, Householder transformation 21
Matrix reduction, Jordan form 45
Matrix reduction, Metzler matrix 46
Matrix reduction, non-negative matrix 45
Matrix reduction, nonsymmetric matrix 43
Matrix reduction, normal matrix 43
Matrix reduction, pairs of matrices 41
Matrix reduction, Perron's theorem 46
Matrix reduction, polar form 70
Matrix reduction, Q-R-decomposition 21
Matrix reduction, rank factorization 19
Matrix reduction, singular value decomposition 43
Matrix reduction, spectral decomposition 40 45 46
Matrix reduction, symmetric matrix 20 39
Matrix reduction, triangular form 20 22
Matrix trace 28 33 65
Matrix unit (or identity) 15
Matrix, adjoint 76
Matrix, Cayley — Hamilton theorem 44
Matrix, conjugate transpose 16
Matrix, eigen values and vectors 3 8
Matrix, elementary 17
Matrix, g-inverse See Matrix inversion
Matrix, gramian 69
Matrix, hermitian 17
Matrix, idempotent 28
Matrix, identity (or unit) 15
Matrix, inverse 16
Matrix, inverse, generalized See Matrix inversion
Matrix, non-negative 45
Matrix, normal 43
Matrix, null 15
Matrix, orthogonal 17
Matrix, partitioned 17
Matrix, symmetric 17
Matrix, transpose 15
Matrix, unitary 17
Matthai, A. 313
Maximum likelihood (m.l.), characterization by m.l. estimators 378
Maximum likelihood (m.l.), distribution of m.l. estimators 365
Maximum likelihood (m.l.), limitation of m.l. method 355
Maximum likelihood (m.l.), m.l. equation estimator 353
Maximum likelihood (m.l.), m.l. estimation of multinomial 355 356—363
Maximum likelihood (m.l.), m.l. estimator 353
Maximum likelihood (m.l.), near m.l. estimator 353
Maximum likelihood (m.l.), properties of m.l. estimator 364
Maximum likelihood (m.l.), scoring for m.l. estimation 366
Maxwell, A.E. 587 603
Mayer, J.W. 160 219
Mayer, M.G. 160 219
Millikin, G.A. 252 313
Minimum trace problems 65—67
Minque theory (variance components) 303
Mitra, S.K. 50 189 220 225 300 313 377 381 504 514 535 603
Moment generating function, binomial 102
Moment generating function, definition 101
Moment generating function, normal 103
Moment generating function, Poisson 102
Moment problem 106
Moore, E.H. 26 78
Moran, P.A.P. 71 78
Moses, L.E. 497 513
Mulholland, H.P. 71 78
Multinomial distribution, definition 355
Multinomial distribution, estimation 356—363
Multivariate moments 107
Multivariate normal distribution, bivariate normal 201
Multivariate normal distribution, characteristic function 184 519
Multivariate normal distribution, characterization 525 526 532
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