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Rao R.C. — Linear Statistical Inference and Its Applications
Rao R.C. — Linear Statistical Inference and Its Applications

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Название: Linear Statistical Inference and Its Applications

Автор: Rao R.C.

Аннотация:

This book is classic work on statistical inference remains highly applicable to statistical analysis. The purpose of this book is to present the theory and techniques of statistical inference in a logically integrated and practical form.


Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1973

Количество страниц: 642

Добавлена в каталог: 08.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Aitken, A.      44 78 220 221 312
Aitkinson, F.A.      71 78
Analysis of covariance, concomitant variables      288
Analysis of covariance, illustrative example      291
Analysis of covariance, multivariate      551 561
Analysis of covariance, univariate      289
Analysis of dispersion, definition      548
Analysis of dispersion, distribution of Wilks' $\Lambda$      555 556
Analysis of dispersion, Gauss — Markoff (multivariate)      543
Analysis of dispersion, growth model (multivariate)      561
Analysis of dispersion, test for additional information      551
Analysis of dispersion, test for dimensionality      556
Analysis of dispersion, test for structural relationship      564
Analysis of dispersion, test of linear hypotheses      547—551
Analysis of variance, confidence interval for ratio      241
Analysis of variance, covariance adjustment      289
Analysis of variance, F-test (Fisher)      238 239
Analysis of variance, Gauss — Markoff model      221
Analysis of variance, general Gauss — Markoff model      297
Analysis of variance, interval estimation      237 470
Analysis of variance, minque (variance components)      65—66 258 303
Analysis of variance, one-way classification      244
Analysis of variance, regression      See Regression and association
Analysis of variance, simultaneous confidence intervals      240
Analysis of variance, t-test (Student, Gosset)      237 243
Analysis of variance, test for nonadditivity, general      251
Analysis of variance, test for nonadditivity, Tukey's      249—251
Analysis of variance, two-way classification, variance components      258
Analysis of variance, two-way classification, with equal numbers      247 253
Analysis of variance, two-way classification, with unequal numbers      254
Ancillary information      505
Anderson, S.L.      498 512
Anderson, T. W.      68 78 498 512 542 601
Anscombe, F. J.      426 428 442 485 512
Arnold, J.C.      322 380
Ashton, E.H.      579 601
Bagai      543
Bahadur, R.R.      140 141 153 366 380 425 442 470 512
Banerji, S.      463 512
Barnard, G.      343 444 488 490 505 512
Barnard, M.M.      572 602
Bartlett, M.S.      551 556 559 573 602
Basis of vector space, definition      4
Basis of vector space, Gram — Schmidt orthogonalization      9
Basis of vector space, orthogonal basis      9
Basis of vector space, orthonormal basis      9
Basis of vector space, Steinitz replacement result      14
Basu, D.      505 512
Bayes decision rule      493
Berge, C.      53 78
Bhattacharya, A.      324 376 380
Bickle, P.J.      153
Birch, M.W.      363 380
Birnbaum, A.      444 505 512
Bivariate normal, characteristic function      203
Bivariate normal, density      202
Bivariate normal, distribution of correlation coefficient      206 208
Bivariate normal, distribution of means      205
Bivariate normal, distribution of regression coefficient      208
Bivariate normal, distribution of variances and covariances      205
Bivariate normal, properties      202
Blackwell, D.      321 380 497 512
Bock, R.D.      196 218
Borel field, ($\sigma$-field)      83
Bose, R.C.      220 224 312 542 597 599 602 603
Bowker, A.K.      542 602
Box G.E.P.      286 312 498 512
Burnaby, T.P.      580 602
Central limit theorems, invariance principle      148
Central limit theorems, Liapunov      127
Central limit theorems, Lindberg — Feller      128
Central limit theorems, Lindberg — Levy      127
Central limit theorems, multivariate case      128 147
Chakravarthy, I.M.      509
Chapman, D.G.      324 380
Characteristic function of, beta      151
Characteristic function of, binomial      102
Characteristic function of, Cauchy      151
Characteristic function of, degenerate      151
Characteristic function of, gamma      151
Characteristic function of, hyperbolic      151
Characteristic function of, Laplace      151
Characteristic function of, multivariate normal      184 519 520
Characteristic function of, normal      103 159
Characteristic function of, Poisson      102
Characteristic function of, rectangular      151
Characteristic function of, triangular      151
Characteristic function, Bochner's theorem      141
Characteristic function, Continuity Theorem      119
Characteristic function, convergence of      119
Characteristic function, cumulants      101
Characteristic function, definition      99
Characteristic function, examples on      142—143
Characteristic function, expansion of      100
Characteristic function, inversion theorem      104
Characteristic function, moments      93 101
Characteristic function, non-negative definiteness of      141
Characteristic function, properties of      100
Chernoff, H.      441 442 453 464 470 482 497 504 513
Chipman, J.S.      307 312
Cluniess-Ross      573 603
Cochran, W. G.      189 218 266 286 312 393 442 464 504 513
Conditional density      92 99
Conditional expectation      96 98
Conditional probability      90
Conditional variance      97
Confidence sets and intervals      470
Constantine, A.G.      543
Contingency tables, control charts (O.C. of)      510
Contingency tables, Dandekar's continuity correction      414 415
Contingency tables, test for independence of attributes      404—415
Contingency tables, Yates' continuity correction      413 415
Control charts (O.C. of)      510 511
Convergence of densities (Scheffe)      124—126
Convergence of distribution functions in law      116
Convergence of distribution functions, definition      116
Convergence of distribution functions, extended Helly — Bray theorem      118
Convergence of distribution functions, Helly lemma      117
Convergence of distribution functions, Helly — Bray theorem      117
Convergence of distribution functions, Polya's theorem      120
Convergence of distribution functions, theorems involving moments      121
Convergence of distribution functions, weak compactness      117
Convergence of functions      134
Convergence of integrals, dominated convergence theorem      136
Convergence of integrals, dominated convergence theorem (Pratt's extension)      136
Convergence of integrals, Fatou's lemma      135
Convergence of integrals, monotone convergence theorem      135
Convergence of random variables in law      116
Convergence of random variables in probability      110
Convergence of random variables with probability one      110
Convergence of random variables, almost sure (strong)      110
Convergence of random variables, quadratic mean      110
Convergence of random variables, rth mean      148
Convergence of random variables, theorems on      122—124 148
Convex sets, definition      51
Convex sets, separation theorems      51 52
Convolution of distribution functions      103
Correlation      See Regression
Covariance adjustment      See Analysis of covariance
Cox, D.R.      505 513
Cox, G.M.      286 312 464 504 513
Craig, А.Т.      189 210 218
Cramer, H.      106 137 153 162 218 324 380 517 602
Critical difference      246
Critical region      445
Cumulants      101
Dandekar's continuity correction      414 415
Daniels, H.E.      366 380
Dantzig, G.В.      455 486 513
Darmois, G.      218
DasGupta, S.      68 78
David, F.N.      220 313
Decision theory (identification), admissible rules      492
Decision theory (identification), Bayes' solution      492 493
Decision theory (identification), complete class (minimal)      495
Decision theory (identification), minimax rule      496
Decision theory (identification), non-randomized rule      491
Decision theory (identification), randomized rule      491
Dempster, A.P.      196 218 340 380
Density, Arc sine      165
Density, Bessel function      217
Density, beta (central)      151 165 167 168
Density, beta (noncentral)      172 217
Density, binomial      88 102 155
Density, bivariate Cauchy      170
Density, bivariate normal      201
Density, Cauchy      151 170
Density, chi-square (central)      166 181
Density, chi-square (noncentral)      182
Density, circular normal      174 177
Density, correlation coefficient (non-null)      208
Density, correlation coefficient (null)      207
Density, degenerate      151
Density, directional data      175
Density, Dirichlet      215
Density, equilibrium state of particles      172
Density, exponential family      195
Density, F (noncentral), Fisher      216
Density, f(central)      165
Density, f(noncentral)      172 216
Density, gamma      151 164
Density, geometric      88
Density, Hotelling's $T^2$ (null)      542
Density, Hyperbolic cosine      151
Density, hypergeometric      88
Density, Laplace      151 212
Density, life testing model      213
Density, logarithmic      88
Density, logistic      213
Density, lognormal      212
Density, Makeham's law      214
Density, Maxwell      173
Density, multinomial      355
Density, multiple correlation (central)      273
Density, multiple correlation (noncentral)      599 600
Density, multivariate normal      184 194 527
Density, negative binomial      88
Density, normal      88
Density, order statistics      214
Density, Pareto      212
Density, Pearson $P_{\lambda}$      168
Density, Pearsonian curves      213
Density, Poisson      88 102
Density, Rayleigh      164
Density, rectangular      151
Density, regression coefficient      208
Density, Student's t (central)      170 183 197
Density, Student's t (noncentral)      171
Density, symmetric normal      196
Density, triangular      151
Density, Von Mises      177
Density, waiting time      166
Density, Weibull      214
Density, Wishart      597 598
Density, wrapped-up distributions      178
Density, z (Fisher)      167
Determinantal equation      38
Determinants      22 31
Dewess, G.      304 312
Dharmadhikari, S.W.      106 153
Discriminatory analysis, discriminant scores      574
Discriminatory analysis, discrimination of composite hypotheses      580
Discriminatory analysis, Fisher's discriminant function      567
Discriminatory analysis, sufficiency of discriminant function      578
Discriminatory analysis, tests on discriminant functions      568 569 601
Dispersion matrix      107 517
Distribution free methods      499
Distribution function, conditional      91
Distribution function, convergence      See Convergence of distribution functions
Distribution function, convolution of      103
Distribution function, decomposition of      85
Distribution function, definition      84
Distribution function, properties of      85—87
Distributions (sampling, asymptotic), $X^2$ for contingency tables      403 404—412
Distributions (sampling, asymptotic), $X^2$ for goodness of fit (Pearson)      391
Distributions (sampling, asymptotic), deviation in a single cell      393
Distributions (sampling, asymptotic), deviation in specified cells      397
Distributions (sampling, asymptotic), fractiles      423—425
Distributions (sampling, asymptotic), functions of statistics      385—388
Distributions (sampling, asymptotic), H-test for homogeneity      389
Distributions (sampling, asymptotic), Kolmogorov — Smirnov test      421
Distributions (sampling, asymptotic), likelihood ratio tests (Neyman — Pearson)      417
Distributions (sampling, asymptotic), linear functions of frequencies      383 384
Distributions (sampling, asymptotic), quadratic function of frequencies      384
Distributions (sampling, asymptotic), scoring test (Rao)      417
Distributions (sampling, asymptotic), standard errors      386—388
Distributions (sampling, asymptotic), Wald's large sample tests      417 419
Distributions (sampling, asymptotic), Wilk's $\Lambda$      556
Distributions (sampling, exact), $P_{\lambda}$ (Pearson)      168
Distributions (sampling, exact), (U-statistic (additional information, Rao)      554
Distributions (sampling, exact), chi-square (central)      181
Distributions (sampling, exact), chi-square (noncentral)      182
Distributions (sampling, exact), correlation, intraclass (non-null)      200
Distributions (sampling, exact), correlation, intraclass (null)      199
Distributions (sampling, exact), correlation, multiple (non-null)      599 600
Distributions (sampling, exact), correlation, multiple (null)      273
Distributions (sampling, exact), correlation, product moment (non-null)      208
Distributions (sampling, exact), correlation, product moment (null)      207
Distributions (sampling, exact), Fisher's F (non-null)      216
Distributions (sampling, exact), Fisher's F (null)      167
Distributions (sampling, exact), Fisher's z      167
Distributions (sampling, exact), Hotelling's $T^2$ (non-null)      542
Distributions (sampling, exact), Hotelling's $T^2$ (null)      542
Distributions (sampling, exact), Mahalanobis'$D^2$      542
Distributions (sampling, exact), quadratic forms      185—193
Distributions (sampling, exact), regression (bivariate)      208
Distributions (sampling, exact), sample mean and dispersion      537
Distributions (sampling, exact), sample mean and variance      182
Distributions (sampling, exact), square of normal variable      163
Distributions (sampling, exact), Student's t (non-null)      171
Distributions (sampling, exact), Student's t (null)      170
Distributions (sampling, exact), Wishart distribution      597 598
Dodge, H.F.      473 513
Doob, J.L.      79 98 115 153 350 380 421 442
Dugue, D.      366 380
Dwyer, P.S.      75 78
Eigen values (restricted)      50
Eigenvalues      38
Empirical distribution function, convergence (Glivenko)      421
Empirical distribution function, definition      420
Empirical distribution function, Kolmogorov theorem      421
Empirical distribution function, Kolmogorov — Smirnov statistic      421
Empirical distribution function, Smirnov theorem      422
entropy      173
Estimation, BAN estimator      348
Estimation, Bayes' estimator      335
Estimation, biased estimator      332
Estimation, CAN estimator      347
Estimation, confidence set      334 470
Estimation, consistency (Fisher)      345
Estimation, consistency (method)      345
Estimation, consistency (probability)      344
Estimation, efficiency (asymptotic variance)      346
Estimation, efficiency (first order, Rao)      348
Estimation, efficiency (Fisher)      348
Estimation, efficiency (second order, Rao)      352
Estimation, empirical Bayes estimator (Robbins)      336
Estimation, fiducial inference (Fisher)      339
Estimation, general estimation problem      334
Estimation, Haldane's discrepancy      352
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