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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
Posterior distribution, approximation for large samples      215—219
Posterior distribution, computation in stages      147—148
Posterior distribution, convergence to correct value      202—204
Posterior distribution, limiting      191 222—223
Posterior distribution, ratio of values of      220—221
Pratt, J.W.      75 100 115 138 306 456 459 469
Precise measurement      198—201
Precision matrix of multivariate normal distribution      56
Precision matrix of multivariate t distribution      59
Precision matrix of Wishart distribution      59
Precision of normal distribution      38
Precision of t distribution      42
Preferences among gambles      93
Preferences among lotteries      89 92
Preferences among probability distributions      88—90
Preferences among repeated gambles      100
Preferences among rewards      86—88
Prescott, E.C.      389 459
Principle of optimality      278 300
Prior distribution      139
Prior distribution, improper      190—198
Prior distribution, invariant      196
Probability density function      17
Probability density function, joint, of several random variables      18
probability distribution      10
Probability distribution of parameter in decision problem      121—122
Probability distribution of parameter in decision problem, use of inappropriate distribution      127—128 see "Prior
Probability distribution, multivariate      18
Probability distribution, univariate      17
Probability distributions of rewards, bounded      90
Probability distributions of rewards, bounded, equivalence relations for      107—109
Probability distributions of rewards, unbounded      110—115
Probability function      17
Probability function, joint, of several random variables      18
Probability space      10
Product space      8
Pure decision      129
Purves, R.      394 454
Quisel, K.      405 459
Radner, R.      115 433 459
Raiffa, H.      82 115 138 141 142 159 164 236 249 259 457 459 460
Ramsey, F.P.      75 81 460
Random number of observations      273—275 288 347
Random sample      20 29
Random sample from distribution with unknown parameter      157
Random sample of random vectors      23
Random variable      16
Random vector      22
Randomization      129—130
Randomized decision      128
Rank of a matrix      21
Rao, C.R.      5 27 57 203 210 251 253—255 460
Rao, M.M.      237 451
Ray, S.N.      297 306 450 460
Real line      8
Recall      see "Sampling with recall" "Sampling
Rees, D.H.      249 454
Regression coefficient      256
Regular sequential decision procedure      289
Regular stopping rule      347
Regular supermartingale      365
Regular supermartingale, minimal      368
Reichenbach, H.      4 460
Relative likelihood      70—85
Relative likelihood, agreement with probability distribution      70 78
Relative likelihood, conditional      81—82
Relative likelihood, transitivity of      71
Renyi, A.      433 460
Reward function for Markov process      370
Reward function for Markovian decision process      386
Rewards      86
Rewards in decision problem      121
Rewards, cofinal sequence of      111
Rewards, complete ordering of      87—88
Rewards, interval of      90 110
Rewards, preferences among      86—88
Rewards, probability distributions of      88—89
Rewards, probability distributions of, bounded      90 107—109
Rewards, probability distributions of, preferences among      88—90
Rewards, probability distributions of, unbounded      110—115
Rewards, set of      86
Risk averter      99
Risk function      138
Risk in decision problem      122
Risk in statistical decision problem      137
Risk taker      99
Robbins, H.      293 297 331 335 336 353 365 368 391 404 405 451 455 458—460
Roberts, C.D.      469
Roberts, H.V.      82 460 469
Ross, S.M.      390 453 460
Royden, H.L.      468
Ruben, H.      365 460
Rubin, H.      249 456 468
Sacks, J.      237 297 335 452 456 460
Sacksteder, R.      439 459 460
Sakaguchi, M.      336 433 439 460
Sample space      7
Sample space of composite experiment      8
Sampling cost      see "Cost of observation"
Sampling plan      272 see
Sampling plan and stopping sets      273
Sampling with recall      335
Sampling with recall from normal distribution      341—345
Sampling with recall, existence of optimal stopping rule      349—353
Sampling without recall      331—334
Sampling without recall from normal distribution      336—341
Sampling without recall, bounded procedures      332—333
Sampling without recall, existence of optimal stopping rule      349—353
Sampling without recall, unbounded procedures      333—334
Samuel, E.      391 461
Samuels, S.M.      331 451
Savage, L.J.      4 75 81 93 100 115 138 159 199 240 316 394 452 454 455 461 468
Sawaragi, Y.      422 461
Scarf, H.      411 448 461 470
Scheffe, H.      159 198 457 461
Schlaifer, R.      115 138 141 142 159 164 236 249 259 459—461
Schleifer, A., Jr.      249 449
Schwartz, L.      204 461
Schwartz, R.      469
Schwarz inequality      254
Schwarz, G.      297 461
Scott, D.      81 461
Search problem      423—429
Search problem for Markov chain      442 443
Search problem with equal costs      427—429
Secretary problem      325
Seidenberg, A.      75 456
Sequential decision function      272
Sequential decision problem      272
Sequential decision problem, stable      301
Sequential decision procedure      272
Sequential decision procedure and stopping variable      287—288
Sequential decision procedure, Bayes      276
Sequential decision procedure, bounded      277
Sequential decision procedure, bounded, as approximation to optimal procedure      294—297
Sequential decision procedure, bounded, optimal      278—280
Sequential decision procedure, regular      289
Sequential decision procedure, total risk of      275
Sequential decision procedure, truncation of      294
Sequential decision procedure, unbounded      287
Sequential probability-ratio test      306—316
Sequential probability-ratio test, number of observations      311—312
Sequential probability-ratio test, number of observations, expectation of      313—314
Sequential probability-ratio test, optimal properties of      316
Sequential probability-ratio test, probabilities of decisions      309—311
Sequential probability-ratio test, risk of      315
Sequential probability-ratio test, risk of, for small sampling cost      315—316
Sequential sample      267
Sequential sample, gain from      267—271
Sequential sample, sequential random sample      272 346
Sequential selection of experiments      430—432
Shannon, C.E.      431 461
Shaw, L.G.      470
Shelly, M.W., II      411 461 470
Shiryaev, A.N.      306 454 470
Siegel, S.      96 451
Siegmund, D.O.      353 461 470
Simon, H.A.      41 418 461
Singular matrix      21
Skibinsky, M.      470
Smith, C.A.B.      470
Smokier, H.E.      81 456
Snell, J.L.      353 368 372 456 462 470
Sobel, M.      297 462
Springer, B.G.F.      259 462
Springer, M.D.      470
Square matrix      21
St. Petersburg paradox      95
Stable estimation, principle of      199
Stable sequential decision problem      301—306
Standard deviation      24
Standard normal distribution      38
Standardized t distribution      42
Staroverov, O.V.      429 462
State space of Markov process      370
Stationary procedure for inventory problem      409
Stationary procedure for Markovian decision process      389
Stationary stopping rule      372 373
Stationary transition probabilities      370
Statistic      155
Statistical decision problem, components of      136
Statistical decision problem, components of, and sequential choice of experiments      429—431
Stein, C.      164 193 237 311 455 462
Steinhaus, H.      470
Stochastic transformation      434
Stone, M.      196 259 462 470
Stopping rule      272 347
Stopping rule for martingales      356—365
Stopping rule for search problem      428
Stopping rule, regular      347
Stopping variable      288 347
Strassen, V.      439 462
Strauch, R.E.      389 390 462
Strong Law of Large Numbers      203
Subjective probability      4 69—85
Subjective probability and relative likelihood, agreement of      70 77—78
Subjective probability, auxiliary experiment for construction of      75—77
Subjective probability, uniqueness of      80—81
Submartingale      354
Submartingale, stopping rules for      356—365
Sufficient experiment      433—439
Sufficient experiment, optimality of      437
Sufficient statistics      155—159
Sufficient statistics for exponential family      161
Sufficient statistics, factorization criterion for      156
Sufficient statistics, jointly sufficient statistics      158
Sunahara, Y.      422 461
Supercontinuous functions      205
Supercontinuous functions, convergence of      210
Supermartingale      354
Supermartingale and optimal stopping rule      365—369
Supermartingale, minimal      368
Supermartingale, regular      365
Supermartingale, regular, minimal      368
Supermartingale, stopping rules for      356—365
Suppes, P.      82 96 100 115 451 457 462 470
Supporting hyperplane      131
Suzuki, Y.      470
Symmetric matrix      22
t distribution      41 249
t distribution, as marginal prior distribution      170
Tan, W.Y.      259 462 470
Teicher, H.      336 365 451 452 462
Testing hypotheses, problems of      237
Testing hypotheses, problems of, in linear model      253
Testing hypotheses, problems of, in linear model, about regression coefficients      256
Testing hypotheses, problems of, sequential      297
Thatcher, A.R.      470
Theil, H.      418 462 470
Thompson, J.W.      470
Thompson, W.E.      470
Thompson, W.R.      404 462
Thorp, E.O.      394 462
Thrall, R.M.      115 462
Tiao, G.C.      259 462 464 466 468 470
Tingey, F.H.      470
Total risk      142
Total risk of sequential decision procedure      275
Total risk, behavior of      145
Tou, J.T.      422 463
Trace (Tr)      22
Transformation of random variables, one-to-one      27
Transformation of random variables, probability integral      31
Transformation of random variables, stochastic      434
Transition function for Markovian decision process      386
Transition function of Markov process      370
Truax, D.      469
Tucker, H.G.      5 463
Tversky, A.      467
Tweedie, M.C.K.      365 463
Two-armed-bandit problem      394—405
Two-armed-bandit problem with dependent parameters      399—404
Two-armed-bandit problem with one parameter known      396—399
Uncertainty function      431
Uniform distribution      40
Uniform distribution and construction of subjective probability      76—77
Uniform distribution and sufficient experiment      437
Uniform distribution as approximation to prior distribution      198—201
Uniform distribution in inventory problem      440
Uniform distribution, conjugate family for      172 173
Uniform distribution, estimation problem for      260
Uniform distribution, estimation problem for, sequential      322—323
Uniform distribution, improper      191 197
Uniform distribution, improper prior distribution for      222 224
Uniform distribution, improper, invariance of      196
Uniform distribution, sampling without recall      380 381
Uniform distribution, sequential decision problem for      318 323
Uniform distribution, sufficient statistics for      158 184
Uniformly integrable sequence      359
Union of sets      7
Utility      86—118
Utility function      90
Utility function for ranks in optimal stopping problem      326 327
Utility function in decision problem      122
Utility function, axiomatic development of      101—115
Utility function, bounded      109—110 115
Utility function, concave      99
Utility function, concave in betting problems      393—394
Utility function, convex      99
Utility function, convex in betting problems      391—393
Utility function, linear transformation of      91 108
Utility function, measurability of      106—107
Utility of gambling      94
Utility of insurance policy      99—100
Utility of monetary gain      95-101
Utility of monetary gain, difficulties in measurement of      94
Utility of probability distribution      91
Utility of reward      91
Utility, experimental measurement of      95—96
Vagholkar, M.K.      470
Vague prior information      190—191 193
Vague prior information in estimation problem      230 231 233 235
Vague prior information in testing hypotheses      240
van der Velde, E.A.      394 458
van Eeden, C.      469
Van Ryzin, J.R.      391 455 463
Vande Linde, V.D.      423 463
Variance      23
Veinott, A.F., Jr.      390 411 452 463
Ville, J.      356 463
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