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| Авторизация |
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| DeGroot M.H. — Optimal statistical decisions |
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| Предметный указатель |
Generalized probability density function, conditional 28
Generalized probability density function, joint, of several random variables 19
Generalized probability density function, marginal 20
Geometric distribution 36
Ghosh, J.K. 297 316 454 468
Ghosh, M.N. 468
Ghurye, S.G. 468
Gilbert, J.P. 331 333 454
Gilford, D. 411 461
Girshick, M.A. 115 138 236 272 293 316 439 444 448 449 468
Gnedenko, B.V. 5 454
Good, I.J. 4 237 454 468
Graybill, F.A. 5 459
Grettenberg, T.L. 468
Grigelionis, B.I. 306 454
Grizzle, J.E. 469
Grundy, P.M. 249 454
Gupta, S.S. 62 454
Guthrie, D., Jr. 468
Guttman, I. 333 454 468
Hackleman, R.P. 433 454
Hadley, G. 138 411 454
Haggstrom, G.W. 353 368 454 468
Hald, A. 468
Hall, W.J. 468
Halmos, P.R. 9 159 206 455
Hannan, J.F. 391 455
Harris, B. 5 455
Harris, T.E. 410 448
Hartigan, J. 196 455 468
Healy, M.J.R. 249 454
Herstein, I.N. 115 455
Hildreth, C. 468
Hill, B.M. 259 455 468
Hodges, J.L., Jr. 468
Hoeffding, W. 306 455 468
Hoel, P.G. 469
Hogg, R.V. 5 455
Holland, J.D. 138 455
Hotelling's  distribution 198
Howard, R. 390 455
Hunter, W.G. 467
Huzurbazar, V.S. 210 455
Hypergeometric distribution 36
Hypergeometric distribution, prior distribution for 187—188
Hyperplane 131
Hypothesis 237 238
Improper prior distribution 190—198 222—224 see
Improper prior distribution in estimation problem 237
Improper prior distribution in linear model 252
Independence of events 10
Independence of random variables 20
Information matrix 216
Information number 316
Information, amount of 432—433
Integrable function 19
Integral, abstract 89
Integral, abstract, Lebesgue — Stieltjes 19
Intersection of sets 7
Invariant prior distribution 196
Inventory problem 405—411
Inventory problem with infinite number of stages 408—410
Inverse of a matrix 22
Isbell, J.R. 404 455
Jackson, J.E. 272 455
James, W. 237 455
Jeffreys, H. 4 193 196 219 243 455
Jenkins, G.M. 164 448 466
Jensen's inequality 97 436
Johns, M.V., Jr. 391 455 468
Johnson, N.L. 313 455
Johnson, R.A. 216 455
Johnson, S.M. 404 449
Jones, W. 465
Kadane, J.B. 429 455
Karlin, S. 249 390 404 411 432 448 449 455 468 469
Kaufman, G.M. 183 447
Kelly, J.L., Jr. 394 456
Kemeny, J.G. 372 456
Kemp, K.W. 469
Kempthorne, O. 433 456
Kerridge, D.F. 469
Keynes, J.M. 4 456
Khinchin, A.I. 431 456
Kiefer, J. 297 316 410 452 456 469
Kleindorfer, G.B. 423 456
Kleindorfer, P.R. 423 456
Knapp, A.W. 372 456
Kolmogorov, A.N. 9 206 456
Koopman, B.O. 81 161 456
Koopmans, T.C. 115 456
Kraft, C.H. 75 456 469
Krickeberg, K. 5 292 456
Kullback, S. 316 433 456
Kulldorff, G. 210 456
Kyburg, H.E., Jr. 81 456
Law of Large Numbers 203
Le Cam, L. 216 293 439 456 469
Least-squares estimate 250
Lebesgue dominated convergence theorem 206
Lechner, J.A. 297 457 469
Lehmann, E.L. 118 238 316 404 439 444 457 468 469
Levy, P. 356 457
Likelihood equation 209
Likelihood equation for vector parameter 217
Likelihood function 164 201
Likelihood function, approximation for large samples 212—219
Likelihood relation see "Relative likelihood"
Lindgren, B.W. 5 457
Lindley, D.V. 182 193 216 219 243 287 331 432 457 469
Lindman, H. 199 240 452
Line of support 98 132
Linear model 250
Linnik, Yu.V. 224 457
Location parameter of t distribution 42
Location vector of multivariate t distribution 59
Lofeve, M. 5 203 206 292 356 457
Lorden, G. 297 457
Loss function 122
Loss function in estimation problem 226 227
Loss function in estimation problem, absolute value of the error 231—233
Loss function in estimation problem, quadratic 227—231 234
Loss function, nonnegativity of 124—125
Lottery 89 92
Luce, R.D. 82 100 115 457 469
MacQueen, J. 335 390 394 457
Maitra, A. 390 458 465
Mallows, C.L. 405 433 458
Mandelbrot, B. 41 458
Manne, A. 469
Marginal distribution 20
Markov chain 370
Markov chain in search problem 442 443
Markov process 369 370
Markovian decision process 386—391
Markovian decision process with infinite number of stages 388—390
Marks, B.L. 469
Marriage problem 325
Marschak, J. 96 100 115 390 410 433 448 458
Martin, J.J. 390 458
Martingale 354
Martingale, formed from products 354 363—364
Martingale, formed from sums 354 361 363 365
Martingale, stopping rules for 356—365
Matrix 21
Matthes, T.K. 316 458
Matula, D. 429 458
Maximum likelihood estimator 210 235—236
Maximum likelihood estimator, asymptotic distribution of 219
McCall, J.J. 336 458
| McCord, J.R., III 5 458
Mean 23 see
Mean vector 24
Measurability of utility function 106
Measurable function 10
Median 231 232
Merrill, J.A. 470
Messick, S. 469
Meyer, P.A. 356 458
Mikhalevich, V.S. 297 458
Miller, H.D. 365 458
Miller, R.G., Jr. 335 458
Milnor, J. 115 455
Minimax decision 136
Mitten, L.G. 466
Mixed decisions 128
Mixed decisions, space of 129
Mixed distribution 17
Mixed distribution, joint, of several random variables 18
Miyasawa, K. 433 458
Molenaar, W. 394 458
moment 23
Moment-generating function 26
Monotone case for optimal stopping 368
Monotone statistical decision problem 249
Mood, A.M. 5 459
Morgenstern, O. 115 136 138 463
Moriguti, S. 297 331 451 459
Moroney, R.M., Jr. 5 458
Morse, N. 439 459
Moser, L. 333 459
Moses, L.E. 115 138 450
Mosteller, F. 36 96 331 333 454 459
Multidecision problem 249
Multinomial distribution 48
Multinomial distribution, conjugate family for 174
Multinomial distribution, estimation problem for 262
Multinomial distribution, improper prior distribution for 222
Multinomial distribution, testing hypotheses about 263
Multiple linear regression 250
Multivariate distribution 18
Multivariate normal distribution 51
Multivariate normal distribution as approximation to multivariate t distribution 255 256
Multivariate normal distribution as approximation to posterior distribution 217—219
Multivariate normal distribution as prior distribution 175
Multivariate normal distribution in control problem 419
Multivariate normal distribution in linear model 250
Multivariate normal distribution, confidence set for 197 198
Multivariate normal distribution, conjugate family for 175—183
Multivariate normal distribution, improper prior distribution for 196—198 223—224
Multivariate normal distribution, limiting posterior distribution for 197
Multivariate normal distribution, ratio of values of p.d.f. 220
Multivariate normal distribution, singular 53
Multivariate normal distribution, sufficient statistics for 184—185
Multivariate normal-gamma distribution 183
Multivariate normal-Wishart distribution 178—179
Multivariate t distribution 59
Multivariate t distribution as limiting posterior distribution 223
Multivariate t distribution as marginal posterior distribution 180
Multivariate t distribution in linear model 252 253
Myopic procedure, optimality of, for Markov process 377
Myopic procedure, optimality of, for sampling with recall 345 381
Myopic procedure, optimality of, for search problem 428
Myopic procedure, optimality of, for two-armed-bandit problem 399 402
Myopic procedure, optimality of, in monotone case 368
Nadler, J. 316 451
Nagel, E. 4 459
Nakamizo, T. 422 461
Negative binomial distribution 35
Negative binomial distribution, conjugate family for 165
Neveu, J. 356 459
Neyman — Pearson lemma 146
Neyman, J. 130 219 459
Nogee, P. 96 459
Nonnegative definite matrix 22
Nonsingular matrix 21
Normal distribution 37 263
Normal distribution and sufficient experiment 439 445
Normal distribution as approximation to likelihood function 213
Normal distribution as approximation to posterior distribution 215
Normal distribution as prior distribution 167
Normal distribution in control problem 415—416
Normal distribution in linear model 250
Normal distribution in two-armed-bandit problem 440
Normal distribution, confidence interval for 193—195
Normal distribution, conjugate family for 166—172
Normal distribution, estimation problem for 232—233 235 260 262
Normal distribution, estimation problem for, sequential 284—285
Normal distribution, improper prior distribution for 191 194-196
Normal distribution, limiting posterior distribution for 191 194 195
Normal distribution, ratio of values of p.d.f. 220—221
Normal distribution, sampling with recall 341—345
Normal distribution, sampling without recall 336—341 381
Normal distribution, sequential probability-ratio test for 322
Normal distribution, sufficient statistics for 157 158 184
Normal distribution, testing hypotheses about 239—243 247—249
Normal distribution, testing hypotheses about, sequential 286—287 298—300
Normal equations 251
Normal form of analysis 142
Normal-gamma distribution 169—170
Novick, M.R. 469
Nuisance parameter 227
Observation error 414
one-way analysis of variance 257
Optimal sequential decision procedure 276
Optimal sequential decision procedure with fixed number of observations 285
Optimal sequential decision procedure, approximation by bounded procedure 294—297
Optimal sequential decision procedure, asymptotic study of 297
Optimal sequential decision procedure, existence of 290—293
Optimal sequential decision procedure, regions for continuing or terminating sampling 297—298
Optimal stopping 324
Optimal stopping and one-armed bandit problem 405
Optimal stopping for Markov process 371—376
Optimal stopping for sampling with recall 335
Optimal stopping for sampling with recall from normal distribution 341—345
Optimal stopping for sampling without recall 331—334
Optimal stopping for sampling without recall from normal distribution 336—341
Optimal stopping for selecting reward of highest rank 325—331
Optimal stopping in two-armed-bandit problem 397
Optimal stopping rule 325
Optimal stopping rule, existence of 345—349
Optimal stopping rule, existence of, for sampling with recall and without recall 349—353
Order statistics 21 31
Orford, R.J. 469
p.d.f. see "Probability density function"
p.f. see "Probability function"
Page, E.S. 469
Papoulis, A. 5 459
PARAMETER 29
Parameter in decision problem 122
Parameter of conjugate family 160—161
Parameter space 122
Pareto distribution 41
Pareto distribution as prior distribution 172
Pareto distribution, sampling without recall 380 381
Parzen, E. 5 36 459
Peterson, R.P. 469
Pfanzagl, J. 469
Pfeiffer, P. 5 459
Pitman, E.J.G. 161 459
Plackett, R.L. 469
Poisson distribution 35
Poisson distribution, conjugate family for 164
Poisson distribution, estimation problem for 229 230 262
Poisson distribution, improper prior distribution for 222
Poisson distribution, sequential probability-ratio test for 322
Poisson distribution, sufficient statistics for 183—184
Positive definite matrix 22
Posterior distribution 139
Posterior distribution and sampling methods 166
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