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| Авторизация |
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| Rao R.C. — Linear Statistical Inference and Its Applications |
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| Предметный указатель |
Multivariate normal distribution, definition 184 518 522
Multivariate normal distribution, density (nonsingular dispersion) 184 194 517 527
Multivariate normal distribution, density (singular dispersion) 527
Multivariate normal distribution, estimation of parameters 528
Multivariate normal distribution, properties of 519—524
Multivariate normal distribution, symmetric 197
Munroe, M.E. 84 137 154
Nair, U.S. 555 603
Neyman, J. 220 266 313 352 366 381 417 442 444 445 470 504 514
Nievergelt, E. 501 514
Noether, G.E. 470 514
Nonparametric inference, distribution free method 499
Nonparametric inference, Fisher — Yates test 501
Nonparametric inference, permutation distribution 503
Nonparametric inference, randomization principle 501
Nonparametric inference, robustness 497
Nonparametric inference, sign test 500
Nonparametric inference, Van der Waerden test 501
Nonparametric inference, Wald — Wolfowitz test 500
Nonparametric inference, Wilcoxon test 500
Nordskog, A.W. 287 313
Normal distribution (characterization), Cramer's theorem 162
Normal distribution (characterization), Darmois — Skitovic theorem 218
Normal distribution (characterization), De Moivre's theorem 160
Normal distribution (characterization), Hagen's hypothesis 161
Normal distribution (characterization), Herschell's hypothesis 158
Normal distribution (characterization), maximum entropy 162
Normal distribution (characterization), Maxwell's hypothesis 160
Normal distribution (characterization), other theorems 218
Normal distribution (characterization), Polya's theorem 215 216
Normal distribution, characteristic function 103 159
Normal distribution, circular normal 174 177
Normal distribution, moment generating function 101
Ogasawara, Т. 188 189 219
Ogawa, J. 189 210 219
Okamoto, M. 125 154
Order statistics 214 410
Orthogonal basis of a random variable 587
Parthasarathy, K. 79 154
Parzen, E. 220 313
Pathak, P.K. 142 154 218 219
Patil, G. P. 377 381
Pearson, E.S. 313 417 442 445 514
Pearson, Karl 213 281 284 313 391 443
Penrose, R. 26 78
Perlman, M.D. 333 381
Permutation distribution 503
Pillai, R.N. 218 219
Pillai, S.S. 543
Pitman, E.J.G. 470 504 513
Plackett, R. L. 286 313 499 514
Poti, S.J. 456
Pratt, J.W. 136 154
Principal components 590
Probability generating functions, binomial 102
Probability generating functions, convergence of 126
Probability generating functions, definition 101
Probability generating functions, Poisson 102
Probability, axioms 82
Probability, conditional 90
Probability, density (p.d.) 87 89
Probability, family of measures 130
Probability, generating function 101
Probability, independence 90
Probability, measure 83
Probability, posterior 334
Probability, prior 334
Probability, space 84
Prohorov, Yu. V. 518 603
Projection operator, definition 46
Projection operator, explicit expressions 47 48
Projection operator, orthogonal 10 47
Puri, M.L. 501 514
Quadratic forms, classification 35
Quadratic forms, distribution of 185—193
Quadratic forms, extremum problems 60—65
Quadratic forms, reduction of one form 20 40
Quadratic forms, reduction of two forms 41
Quadratic forms, transformation 35
Ramachandran, В. 79 154
Random variables, conditional distribution 91
Random variables, convergence See Convergence of random variables
Random variables, definition 84 87 89
Random variables, independence of 92
Random variables, Kolmogorov consistency theorem 108
Randomization principle 501
Rao, J.S. 178 219
Rao, K.S. 542 603
Rasch, G. 587 603
Regression (examples), cranial capacity 270
Regression (examples), equality of coefficients 281
Regression (examples), specification (test of) 284
Regression and association, best linear predictor 266 267
Regression and association, best predictor 264
Regression and association, canonical correlations 582
Regression and association, canonical variables 584
Regression and association, common factors 585
Regression and association, correlation ratio 265
Regression and association, covariance analysis 289
Regression and association, factor analysis 587
Regression and association, general theory of 263—270
Regression and association, intraclass correlation 268
Regression and association, linear predictor 266 267
Regression and association, multiple correlation 266 268
Regression and association, part correlation 311
Regression and association, partial correlation coefficient 268 269
Regression and association, partial correlation ratio 268
Regression and association, partial multiple correlation 268
Regression and association, restricted coefficients 287
Renyi, A. 143 154
Riffenburgh, R.H. 573 603
Robbins, H. 324 338 380 381 489 490 513
Robustness 497
Romig, H.G. 474 513
Rosenblatt, M. 470 513 518 602
Roy, J. 377 381 556 603
Roy, S.N. 542 561 573 597 599 602 603
Sakamoto, H. 189 210 219
Savage, I.R. 501 514
Savage, L.J. 95 154 444 470 501 504 514
Scheffe, H. 124 154 240 241 286 313 381
Scoring test (Rao) 417 418
Second order efficiency (Rao) 352
Seigmund, D. 488 489 514
Sen, P. K. 501 514
Sengupta, S. 178
Sequential analysis, A. S. N. function 484
Sequential analysis, control charts (O.C. of) 510
Sequential analysis, efficiency of S. P. R. Т. 478
Sequential analysis, estimation (Stein) 485
Sequential analysis, fundamental identity 482
Sequential analysis, O.C. function 484
Sequential analysis, S. P. R. T. (Wald) 475—478
| Sequential analysis, test with power one 488
Sequential analysis, truncation of S. P. R. Т. 510
Shaw, D.C. 270
Siegel, S. 501 515
Singular value decomposition 42
Skitovic, V.P. 218 219
Slater, P. 576
Smirnov,N. 421 422 443
Smith, С.А.В. 71 78 511 513 578 603
Sprott, D.A. 207 340 355 381 444 513
Srivastava, J.N. 573 603
Statistics and subfields 139
Stein, C. 324 343 381 486 515
Stieltje's integral 132
Stirling's approximation 59
Student, (W.S. Gosset) 170 219
Subfield 86 139 141
Sudakov, V. N. 132 154
Sufficient statistic, bounded completeness 457
Sufficient statistic, completeness 321
Sufficient statistic, definition 130
Sufficient statistic, factorization theorem 131
Sufficient statistic, Huzurbazar's conjecture 132
Sufficient statistic, use in estimation (Rao, Blackwell) 321
Sufficient sub-field 141
Sylvester's law (matrix rank) 31
t-test (Student) 170 183 197 237 243 459
Takahashi, M. 188 189 219
Teicher, H. 379 381
Testing of hypotheses (theory), ancillary information 505
Testing of hypotheses (theory), asymptotic efficiency 464
Testing of hypotheses (theory), composite hypothesis 445 456
Testing of hypotheses (theory), critical function 450
Testing of hypotheses (theory), critical region 445
Testing of hypotheses (theory), distribution free methods 493
Testing of hypotheses (theory), Fisher — Behren's problem 463
Testing of hypotheses (theory), level of significance 446
Testing of hypotheses (theory), Lindley's paradox 512
Testing of hypotheses (theory), locally most powerful test 453 454
Testing of hypotheses (theory), monotone likelihood ratio 461
Testing of hypotheses (theory), Neyman — Pearson lemma 446
Testing of hypotheses (theory), nonparametric tests See Nonparametric inference
Testing of hypotheses (theory), permutation test 503
Testing of hypotheses (theory), Pitman efficiency 467
Testing of hypotheses (theory), probability ratio test 451
Testing of hypotheses (theory), randomized test 450
Testing of hypotheses (theory), robustness 498
Testing of hypotheses (theory), sequential test See Sequential analysis
Testing of hypotheses (theory), similar region test 456
Testing of hypotheses (theory), two kinds of errors 445
Testing of hypotheses (theory), unbiased test 454
Testing of hypotheses (theory), uniformly most powerful test 449
Theorems (named after authors), Bayes 334
Theorems (named after authors), Bochner (n.n.d. of characteristic function) 141
Theorems (named after authors), Caley — Hamilton (matrix) 44
Theorems (named after authors), Chebychev (W.L.L.N.) 112
Theorems (named after authors), Cramer (normal) 162
Theorems (named after authors), Darmois — Skitovic 218 526
Theorems (named after authors), DeMoivre 160
Theorems (named after authors), Fieller 311
Theorems (named after authors), Fisher — Cochran 185
Theorems (named after authors), Frobenius (positive matrix) 46
Theorems (named after authors), Fubini 137
Theorems (named after authors), Glivenko 421
Theorems (named after authors), Helly — Bray 117
Theorems (named after authors), Helly — Bray (extended) 118
Theorems (named after authors), Kinchin (W.L.L.N.) 112 146
Theorems (named after authors), Kolmogorov (consistency of distributions) 108
Theorems (named after authors), Kolmogorov (d.f. of  ) 421
Theorems (named after authors), Kolmogorov (S.L.L.N.) 114 115
Theorems (named after authors), Kolmogorov (sums of random variables) 129
Theorems (named after authors), Kolmogorov (W.L.L.N.) 146
Theorems (named after authors), Lebesgue dominated convergence 136
Theorems (named after authors), Lebesgue monotone convergence 135
Theorems (named after authors), Liapunov (C.L.T.) 127
Theorems (named after authors), Lindberg — Feller (C.L.T.) 128
Theorems (named after authors), Lindberg — Levy (C.L.T.) 127
Theorems (named after authors), Perron (positive matrix) 46
Theorems (named after authors), Polya (convergence of d.f.) 120
Theorems (named after authors), Polya (normal law) 215 216
Theorems (named after authors), Pomcare separation 64
Theorems (named after authors), Radon — Nikodym 137
Theorems (named after authors), Sakamoto — Craig 210
Theorems (named after authors), Scheffe 124
Theorems (named after authors), Smimov 422
Theorems (named after authors), Strumian separation 64
Transformation (linear) 23 24
Transformation of statistics, binomial proportion  427
Transformation of statistics, correlation coefficient  {-1})$ 432
Transformation of statistics, Poisson variable  426
Transformation of variables 156
Tukey, J. 249 251 313
TurnbuU, H.W. 44 78
Van der Wearden, B.L. 501 515
Varadarajan, V.S. 128 154 518
Variance and covariance components, general model 302
Variance and covariance components, minque theory 303
Variance and covariance components, two way data 258
Vector space, basis (Hamel) 4
Vector space, definition 3
Vector space, direct sum 11 40
Vector space, Gram — Schmidt orthogonalization 9
Vector space, inner product 8 74
Vector space, orthogonal basis 9
Vector space, orthonormal basis 9
Vector space, subspace 4
Wald's large sample tests 41 419
Wald's S.P.R.T. 475
Wald, A. 124 128 154 366 381 417 443 455 456 474 495 497 500 515 579 603
Walsh, J.E. 501 515
Watson, G.S. 174 219 531 603
Watterson, G.A. 71 78
Weiss, L. 425 443
Welch, W.L. 464 515
Wijsman, R.A. 542 603
Wilcoxon, F. 500 515
Wilks'  criterion, Bartlett's approximation 556
Wilks' criterion, decomposition 554
Wilks' criterion, definition 551
Wilks' criterion, distribution (asymptotic) 556
Wilks' criterion, distribution (exact) 555
Wilks' criterion, variance ratio approximation (Rao) 556
Wilks, S.S. 543 551 555 604
Williams, E.J. 174 219 286 313 573 604
Winston, С.В. 444 505 512
Wishart distribution 533 597 598
Wishart, J. 291 313 573 604
Wold, H. 106 153 517 518 604
Wolfowitz, J. 124 154 363 381 485 500 504 515
Yates' continuity correction 413 415
Yates, F. 286 313 413 443
Zelen, M. 220 312
Zero-one law 148
Zyskind, G. 220 313
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