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| DeGroot M.H. — Optimal statistical decisions |
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| Предметный указатель |
 8
 distribution 39
distribution and sufficient experiment 444
distribution as approximate posterior distribution 219
distribution as limiting posterior distribution 223
 -field 9
A posteriori distribution see "Posterior distribution"
A priori distribution see "Prior distribution"
Abramson, L.R. 432 447
Absolutely continuous distribution 17
Absolutely continuous distribution, multivariate 18
Absorbing state 379
Actuation error 421
Admissible boundary 131
Admissible decision 133
Aggarwal, O.P. 465
Aitchison, J. 465
Albert, A.E. 432 447
Albert, G.E. 465
Allais, M. 93 447
Amount of information 432
Amster, S.J. 306 447
Analysis of variance 257
Anderson, T.W. 52 57 198 316 432 447
Ando, A. 183 447
Andrews, F.C. 365 447
Anscombe, F.J. 81 216 297 448 465
Antelman, G.R. 465
Aoki, M. 422 448
Armitage, P. 465
Arrow, K.J. 293 316 390 410 411 448
Ash, M. 465
Aumann, R.J. 81 115 448
Backward induction 277
Bahadur, R.R. 159 365 448
Barankin, E.W. 465
Barnard, G.A. 138 164 448 466
Barnett, B.N. 287 457
Bartholomew, D.J. 466
Barycentric coordinates 154
Bather, J.A. 287 448 466
Bayes boundary 131
Bayes decision 123 133—136
Bayes decision function 138
Bayes decision function, construction of 138—139
Bayes estimate 227
Bayes risk in decision problem 123
Bayes risk in decision problem, concavity of 125—127 430
Bayes risk in sequential decision problem 294 300 302—306
Bayes risk in sequential decision problem, concavity of 318
Bayes risk in statistical decision problem 138
Bayes risk, asymptotic behavior of 220
Bayes risk, sensitivity to probability distribution of parameter 127—128
Bayes sequential decision procedure 276 see
Bayes' theorem 11 12 28
Bayesian statistical methods 138
Beauty-contest problem 325
Bechhofer, R. 466
Becker, G.M. 96 100 448
Behrens distribution 224
Behrens — Fisher problem 224
Beightler, C.S. 466
Bellman, R. 272 278 301 365 390 404 411 429 448 466
Berk, R.H. 204 449
Berkson, J. 466
Bernoulli distribution 34
Bernoulli distribution, conjugate family for 160
Bernoulli distribution, estimation problem for 260—262
Bernoulli distribution, estimation problem for, sequential 317—319
Bernoulli distribution, improper prior distribution for 222
Bernoulli distribution, sequential probability-ratio test for 322
Bernoulli distribution, sufficient statistics for 157
Bernoulli distribution, testing hypotheses about 263
Bernoulli trials 34 36
Bernoulli, D. 95
Bessler, S.A. 432 449
Beta distribution 40
Beta distribution, as prior distribution 160 165
Beta distribution, limiting values of 222
Betting problems 391—394
Bhat, B.R. 466
Bhattacharya, S.K. 466
Bickel, P.J. 297 449 466
Bilateral bivariate Pareto distribution 62
Bilateral bivariate Pareto distribution as prior distribution 173
Binomial coefficient 12—15
Binomial distribution 34
Birnbaum, A. 164 449 466
Black, W.L. 429 449
Blackwell, D. 115 138 204 236 272 293 316 390 429 434 439 444 448 449 466
Blasbalg, H. 316 449
Bloch, D.A. 219 449
Blum, J.R. 365 447
Bohrer, R. 432 449
Borch, K. 466
Borel set 10
Borel — Cantelli lemma 349
Bounded utility function 109 115
Box, G.E.P. 259 449 466
Bracken, J. 249 449 466
Bradt, R.N. 404 432 449
Braga-Illa, A. 466
Bramblett, J.E. 353 449
Brayfield, A.H. 469
Breakwell, J. 287 450
Breiman, L. 325 372 394 450
Brewer, K.R.W. 82 450
Brown, L. 405 450
Brunk, H.D. 5 450
Bryan, G.L. 470
Bulinskaya, E.V. 466
Burkholder, D.L. 316 450
c.f. see "Characteristic function"
Campling, G.E.G. 471
Carnap, R. 4 450
Cartesian product 8
Cauchy distribution 41
Cayley, A. 333 450
Central limit theorem 37
Chanda, K.C. 217 450
Characteristic function 25
Characteristic function of random vector 26
Cheng, Ping 297 450
Chernoff, H. 115 138 219 220 287 297 315 353 368 405 432 450 466
Chetty, V.K. 259 464
Chew, M.C., Jr. 429 451
Chipman, J.S. 467
Choice of decision 122 123
Choice of decision, methods of choosing 136
Choice of gamble 100
Choice of sample size 145
Chow, Y.S. 293 331 335 336 353 361 365 368 451
Chung, K.L. 372 451
Churchman, C.W. 467
Coefficient of variation 24
Cofinal sequence 111
Cohen, A. 467
Colton, T. 467
Complement of a set 7
Complete ordering of events 72
Complete ordering of probability distributions of rewards 90 109 110 115
Complete ordering of rewards 87
Compound decision problem 390
Concave function 99
Conditional distribution 28
Conditional expectation 28
Conditional likelihood 81—82
Conditional probability 11
Confidence coefficient 193
Confidence interval 192—193
| Conjugate family of distributions 159
Conjugate family of distributions, construction of 161—164
Consistent sequence of statistics 209 211 217
Contingency table 220
Control problem 411—423
Control problem with actuation error 421—422
Control problem with observation error 414—421
Control problem with observation error, multidimensional 418—421
control variable 411
Convex combination 131
Convex function 97
Convex hull 131
Convex set 131
Coombs, C.H. 115 462
Copeland, A.H., Sr. 467
Cornfield, J. 183 454
Correlation 24
Correlation, distribution of 180—182
Cost function for Markov process 370
Cost of observation 142—145
Cost of observation in sequential sample 271—272 276
Covariance 24
Covariance matrix 24
Cox, D.R. 466 467
Craig, A.T. 5 455
Cramer, H. 5 207 210 451
d.f. see "Distribution function"
Darmois, G. 161 451
Davidson, D. 96 451
Davis, R.L. 115 462
de Finetti, B. 75 81 451 467
Debreu, G. 115 451
Decision function 137
Decision function in sequential decision procedure 274
Decision rule in sequential decision procedure 273 274 276
Decision space 121
Degrees of freedom of distribution 39
Degrees of freedom of F distribution 42
Degrees of freedom of multivariate t distribution 59
Degrees of freedom of t distribution 41 42
Degrees of freedom of Wishart distribution 56
Derman, C. 335 390 451
Determinant 21
Deutsch, R. 237 452
Diamond, P.A. 115 456
Dickey, J.M. 467
Dirichlet distribution 49
Dirichlet distribution as prior distribution 174
Dirichlet distribution, limiting values of 223
Discount factor in inventory problem 408
Discount factor in Markovian decision process 388
Discrete distribution 17
Discrete distribution, multivariate 18
Disjoint sets 8
Distribution function 16
Distribution function, joint, of several random variables 18
Distribution function, marginal 20
Doob, J.L. 356 452
Doss, S.A.D.C. 217 452
Draper, N.R. 259 449 467
Dubins, L. 204 336 361 394 449 452
Duncan, D.B. 259 452 467
Dunnett, C.W. 467
Dunsmore, I.R. 467
Dvoretzky, A. 316 336 410 452
Dynamic programming 272
Dynkin, E.B. 159 372 452
Edwards, W. 199 240 452 467
Eggleston, H.G. 131 452
Ehrenfeld, S. 467
Eisenberg, E. 467
Elfving, G. 336 452
Ellison, B.E. 467
Ellsberg, D. 82 94 452
Empirical Bayes procedure 390
Enslow, P., Jr. 429 452
Entrance-fee problem 376—377
Entropy function 431 432
Ericson, W.A. 467
Estimation problem 226—237
Estimation problem for vector parameter 233—235
Ethical neutrality 75 89
Euclidean space 8
Evans, I.G. 237 452
Event 9
Event, ethically neutral 75 89
Expectation 23 90
Expectation and differentiation 207
Expectation, conditional 28
Expected value 23 see
Expected-utility hypothesis 91 95
Expected-utility hypothesis for cost of observation 142
Expected-utility hypothesis for mixed decision 128
Experiment 6
Experiment, sequential selection of 430
Exponential distribution 39
Exponential distribution, conjugate family for 166
Exponential distribution, estimation problem for 261
Exponential distribution, improper prior distribution for 223
Exponential distribution, sampling without recall 380 381
Exponential distribution, sequential decision problem for 318
Exponential family of distributions 161 185
Extensive form of analysis 142
Extreme point 131
F distribution 42
Fabius, J. 204 453
Family of distributions, closed under multiplication 162
Family of distributions, closed under sampling 159
Family of distributions, conjugate 159
Family of distributions, exponential 161
Farrell, R.H. 237 365 453 467
Fatou — Lebesgue theorem 292
Fel'dbaum, A.A. 422 453
Feldman, D. 399 404 453
Feller, W. 5 77 145 203 350 453
Fellner, W. 82 453
Ferguson, T.S. 138 394 436 453
Fishburn, P.C. 81 115 453
Fisher information matrix 216 432
Fisher, L. 390 453
Fisher, R.A. 4 159 164 224 453
Fisz, M. 5 453
Fomin, S.V. 9 206 456
Forced continuation 370 373
Forced stopping 370 378—379
Forced stopping in sampling without recall 382
Fraser, D.A.S. 161 453 468
Freedman, D.A. 204 361 394 452 453
Freeman, H. 5 454
Friedman, M. 100 316 447 454
Functional equation for Bayes risk 300 305
Functional equation for inventory problem 409
Functional equation for Markov process 377—379
Functional equation for Markovian decision process 389
Functional equation for search problem 424
Fundamental identity of sequential analysis 365
Furukawa, N. 405 454
g.p.d.f. see "Generalized probability density function"
Gale, D. 467
Gamble 354 355
Gambling system 360—361
Gambling system and betting problems 391—394
Gamma distribution 39
Gamma distribution as prior distribution 164 166 168
Gamma distribution, sufficient statistics for 184
Gamma function 39
Gart, J.J. 468
Geisser, S. 183 454
Generalized maximum likelihood estimator 236
Generalized probability density function 19
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