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DeGroot M.H. — Optimal statistical decisions
DeGroot M.H. — Optimal statistical decisions

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Название: Optimal statistical decisions

Автор: DeGroot M.H.

Аннотация:

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 489

Добавлена в каталог: 04.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$R^{n}$      8
$\chi^{2}$ distribution      39
$\chi^{2}$ distribution and sufficient experiment      444
$\chi^{2}$ distribution as approximate posterior distribution      219
$\chi^{2}$ distribution as limiting posterior distribution      223
$\sigma$-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 $\chi^{2}$ 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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