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Ferguson T.S. — Mathematical Statistics. A Decision Theoretic Approach
Ferguson T.S. — Mathematical Statistics. A Decision Theoretic Approach

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Название: Mathematical Statistics. A Decision Theoretic Approach

Автор: Ferguson T.S.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1967

Количество страниц: 196

Добавлена в каталог: 07.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\chi^2$-distribut.ion      101 103
$\mathfrak{F}$-distribution      10:3
Absolute error loss      47
Acceptance region      258
Action space      1
Action space, terminal      309
Admissible decision rule      54 70
Admissible decision rule, $\epsilon-$      63
Admissible decision rule, almost      185
Agreeing preference pattern and utility      13
Alternative hypothesis      199
As good as      54
Basu's Theorem      350
Bayes deeision rule      31 37 44 31:3
Bayes deeision rule, $\epsilon-$      32 38
Bayes deeision rule, admissibility of      60 62
Bayes deeision rule, existence of      67
Bayes deeision rule, extended      50
Bayes deeision rule, generalized      50
Bayes deeision rule, limit of      49
Bayes deeision rule, nonrandomized      43 60
Bayes deeision rule, sequential      313 353
Bayes risk      31
Behavioral and randomized rule      24 25
Behavioral and randomized rule,equivalence of      25 26
Behavioral and randomized rule,relation between invariant      151 192
Behavioral strategy      25 26
Bernoulli trials      318 332 338 360 377
Bernoulli trials, dependent      328 340
Best invariant rule      154
Best invariant rule, not minimax      175
Best test      200
Beta distribution      101 223
Beta-binomial distribution      97 100 104 105 328
Better than      54
Binomial distribution      98
Binomial distribution, Bayes estimates for      52 53
Binomial distribution, Bayes sequential estimates for      318ff
Binomial distribution, minimax estimates for      93 95
Bio-assay      123
Bivariate normal distribution      112
Bivariate Poisson distribution      241
Bluffing      3 43 214
Boundary      67
Bounded from below      63
Boundedly complete sufficient statistic      132
Canonical form      266
Cauchy distribution      102 174 236 239 247 298
Chance move      3
Characteristic fundion      99 107
Classification problems      291
Closed from below      64
Closure      64
Compact      84
Complete class of decision rules      55
Complete class of decision rules, essentially      55
Complete class of decision rules, essentially minimal      212
Complete class of decision rules, minimal      55 69
Complete class of decision rules, minimal essentially      55
Complete class theorem      58 87
Complete sufficient statistic      132
Composite hypothesis      206
Confidence ellipsoids      276
Confidence sets      257
Confidence sets, invariant family of      261
Confidence sets, unbiased family of      260
Convex function      76
Convex function, strictly      80
Convex hull      36 65
Convex set      35
Convex set, strictly      75
Correlation coefficient      112
Cost function      310
Covariance matrix      105 106
Critical region      198
Decision function or rule      7
Decision function or rule, behavioral      25
Decision function or rule, best      28
Decision function or rule, equalizer      90
Decision function or rule, invariant      148 341
Decision function or rule, monotone multiple      286
Decision function or rule, nonrandomized      7
Decision function or rule, randomized      24
Decision function or rule, reasonable      29
Decision function or rule, sequential      312
Decision function or rule, terminal      311
Decision problem      7
Decision problem, sequential      315
Decision problemtruncated sequential      315
Diagonal matrix      105
Digamma function      179
Discrimination      295
Dominated family of distributions      116
Double exponential distribution      241 256 378
Dvoretsky — Wald — Wolfowitz theorem      79 142
Equalizer rule      90
Equivalence relation      11 153
Estimation      11 30 46
Estimation of a distribution function      192 348
Estimation of a median      197 350
Exponential distribution      101 180 255 327 349
Exponential family of distributions      126 139 209 217 227
Extended Bayes rule      50 59 87 91
Factorization theorem      115
Fibonacei numbers      339
Fisher — Yates test      252
Fundamental identity      373
Fundamental lemma      201
Fundamental problem of decision theory      28 34
Gambler's ruin      371 378
Game      1
Game, statistical      7
Gamma distribution      52 101 136 181
Gamma function      101
Generalized Bayes rule      50
Geometric distribution      95 99 180 234 327 339
Glivenko — Calltelli lemma      192
Group of trallsformations      143 147
Half-normal distribution      190
Hoelder's inequality      80 128
Hypergeometric distribution      97 99 328
Hypothesis, composite      206
Hypothesis, general linear      264
Hypothesis, null      199
Hypothesis, simple      199
Identifiability      144
Identity transformation      143
Inadmissible decision rule      54
Indicator function      100
Inner product      71
Interior      67
Interval estimate      184
Invariance      30 143
Invariance and convex loss      158
Invariance and sufficiency      157
Invariance in testing hypotheses      242
Invariance of cost      341
Invariance of decision problem      145 341
Invariance of distributions      144 341
Invariance of general linear hypothesis      268
Invariance of loss      145 341
Invariance of prior distribution      162 299
Invariant rules and prior information      152
Inverse probability methods      32
Inverse transformation      143
Jensen's inequality      76 122 331
Laplace transformation      134
Latin square      274
Least favorable distribution      34 39 57 81 90
Least squares      269
Lebesgue integral      7 138
Lebesgue measure      50
Locally best test      235 249 255
Locally best test, one-sided      235
Locally best test, unbiased      237
Location parameter      164
Location parameter, best invariant estimate of      168 186 345
Location parameter, best invariant test for      245
Location parameter, minimax estimate of      171
Location-scale parameter      166 184
Logistic distribution      102 123 215 241 256 200
logit      121
Loss function      1 309
Lower boundary point      64
Lower quantant      63
Lower semicontinuity      84 86
Mann — Whitney test      251
Maximal invariant      243 247 343
Maximum likelihood estimate      123
Mean squared error      11
Minimax decision rule      83 39 57 90
Minimax decision rule, $\epsilon-$      33 39
Minimax theorem      57 82 85
Minimum $\chi^2$ estimate      123
Minimum Bayes risk      31 39
Minimum logit-$\chi^2$ estimate      123
Mixed strategy      23 26
Modal interval      51
Moment generating function      37:3
Monotone likelihood ratio      208 259 286 218 307
Move      2
Multinomial distribution      205
Multiple decision problem      10 284
Multiple decision problem, monotone      285
Natural ordering      54
Natural parameter space      128
Necessary and sufficient statistic      132
Negative binomial distribution      96 99
Neyman structure      227
Neyman — Pearson lemma      201
Neyman — Pearson lemma, generalized      204 238
Noneentral $\chi^2$ , $\mathfrak{F}$, and t-distributions      102 103
Nonnegative definite matrix      80 106
Nonregular families      130 137 259
Nonsingular normal distribution      109
Normal distribution      101
Normal distribution, admissibility of sample mean      141 142 185
Normal distribution, inadmissibility of sample mean      169
Normal distribution, independence of sample mean and variance      115
Normal distribution, invariant estimates for      135 182ff
Normal distribution, minimax estimates for      94 176ff
Normal distribution, multiple decisions for      288 290 294 303ff
Normal distribution, multivariate      107 119 153 169 294
Normal distribution, tests for      207 234 246 249 265ff
Normal distribution, unbiased estimates for      48 122 135
Normal form of game      1
Null hypothesis      199
Objectivists      32
Odd or even      2 8 40 42
One-sided t.est      212 286
One-to-one transformation      143
One-way classification      265 273 280 282
Onto transformation      143
Orbit      149
Order statistics      119 153 192 249 252
Orthogonal group      148 153 244 268
Orthogonal matrix      105
Parameter space      1 309
Payoff      11
Personal probability      17
Pitman estimate      188 247
Poisson distribution      99
Poisson distribution, Bayes estimates for      52 326
Poisson distribution, minimax estimates for      96 327
Poisson distribution, unbiased estimates for      136
Poisson distribution, unbiased tests for      233
Positive definite matrix      106
Power function      198 199 235
Preference pattern      12
Prior distribution      31 37 60
Prior distribution, invariant      162 299
Probability of error      10 200
Pseudo-game      214
Quantile      51
Random stopping time      311
Randomized decisions      22
Randomized decisions, space of      22
Rank test      251
Ranking problems      294
Rao — Blackwell theorem      121 125 331
Rao-Blackwellization      124
Regression      265 273 283
Riemann integral      8 133
Riemann — Stieltjes integral, S      170
Risk function      7 312
Risk set      34 63
Risk set, nonrandomized      36
Rule      see Decision function
Sample distribution function      192 196 348
Sample space      6 310
Scale parameter      164 178 190
Semicontinuity      84
Separating hyperplane theorem      73 82 87
Sequential probability ratio test      361
Sequential probability ratio test, extended      362
Sequential probability ratio test, optimal property of      365 369
Set estimate      283
Similar test      266
Simple function      8
Simple hypothesis      199
Singular normal distribution      109
Size of a test      200 206
Slippage problems      299ff
Spectral theorem      106
Squared error loss      46
Statistical decision problem or game      7
Stopping rule      310
Stopping rule, invariant      341
Strategy      2
Strategy, mixed      23
Subjective probability      17
Subjectivists      32
Sufficiency and invariance      157
Sufficient, sequence      330
Sufficient, statistic      113
Sufficient, statistic, complete class of rules based on      120
Sufficient, statistic, minimal      132
Support of a distribution      61
Supporting hyperplane theorem      73 77
t-distribution      103
t-test      230 232 234 246 263
Terminal action space      309
Terminal decision rule      311
test      198 199
Testing hypotheses      10 198
Three-way classification      274
Tmnsitive group      174
Tramformation      143
Transitive sufficient, sequence      334
Transpose of a vector      71
Two-sided problems      222
Two-sided tests      216
Two-way classification      266 271 281 283
Unbiased estimates      29 48 122 134
Unbiased estimates, sequential      332
Unbiased tests      224ff
Uniform distribution      100
Uniform distribution, Bayes estimates for      45
Uniform distribution, best invariant estimate for      181 185 190 191
Uniform distribution, minimax sequential estimate for      346
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