Govindarajulu Z. — Sequential Statistics :: Электронная библиотека попечительского совета мехмата МГУ

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Govindarajulu Z. — Sequential Statistics

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Название: Sequential Statistics

Автор: Govindarajulu Z.

Аннотация:

This book contains topics that can be covered in a single-semester course. Only elementary proofs are provided, and thus the mathematics and statistics are maintained at a basic level. Only a course in each of three areas — advanced calculus, probability and statistical inference — is assumed of the student. The book has a chapter on applications to biostatistics and a supplement presenting computer programs for selected sequential procedures. Identified problems are provided at the end of each chapter.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 317

Добавлена в каталог: 19.05.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Absolute accuracy      200
Absorbing barriers      36
Acceptance rejection      44
Acceptance sampling      106
Adaptive rule      233
Admissible      2 152
Anderson's test      75
Approximate bounds      16
Approximations to OC and ASN functions      36
Arbitrary continuation region      44
Arbitrary distributions      247
Arbitrary sequential test      33
Arithmatic distribution      87
Armitage's procedure      96
ASN curve      56
ASN function      2 32 36 44 83 85 102
Asymptotic behavior of the stopping time      51
Asymptotic consistency      193 198 201 217
Asymptotic coverage probability      213
Asymptotic efficiency      193 198 201 215 217 219
Asymptotic efficiency, sign test      126
Asymptotic normality      189
Asymptotic normality of the statistic T      66
Asymptotic optimality      152 192 198 201 217
Asymptotic probability of coverage      205
Asymptotic properties      206 235
Asymptotic variance      228 229
Asymptotically risk-efficient      202
Auxiliary problem      19 45
Auxiliary SPRT      53
Average risk      45
Average sample number (ASN)      2 21 24 38 47
B-V procedure      98
Backward induction      111 115 116
Bacterial density      229
BAN (best asymptotically normal) estimates      79
Barnard's criteria      65 73
Barnard's sequential t and -tests      65
Barnard's versions      66
Bartlett's procedure      81
Bayes binomial SPRT      106
Bayes risk      45
Bayes sequential procedure      106
Bayes sequential procedure, normal mean      115
Bayes theorem      107
Bayesian criterion of optimality      144
Behren — Fisher problem      84
Bernoulli case      177
Bernoulli data      269
Bernoulli population      20
Bernoulli variable      22
Best sequential procedure      171
Best unbiased estimate      147
Beta family      112
Binary response      254
Binomial distribution      13
Binomial proportions      85
Bivariate normal distribution      81 208
Boundary values      83
Bounded length confidence intervals      196
Bounds for ASN      33
Brownian motion      50
Brownian motion process      135
Cauchy — Schwarz inequality      154
Central chi-square      8
Central limit theorem      96
Characteristic roots      205 206
Chebyshev's inequality      126
Class of weight functions      72
Closed boundaries      47
Coefficient of variation      171 200
Completeness      145 148 149
Completeness, bounded      145 148
Composite hypothesis      59 75
Composite test      244
Computer program      180
Concave function      52
Confidence coefficient      158
Confidence interval      173
Confidence region      204
Confluent hypergeometric function      65 76
Conjugate prior      112
Consistency property of MLE      240
Continuation point      146
Continuation region      44 60 113 242 245
Continue sampling indefinitely      120
Continue sampling region      17
Continue-sampling inequality      17 83 89
Convergent bounds      271
Cornish — Fisher inversion      173
Correction for overshoot      244
Cost of each observation      45
Cost of experimentation      143
Covariance matrix      204
Covariance structure      208
Coverage probability      176 191 196 211
Cox's procedure      81
Cox's sequential estimation procedure      289
Cramer — Rao inequality      144 148 152
Cramer — Rao inequality, lower bound      144
Cumulative sums      86
Curtailed inspection      3
Curtailed sampling, double      148
Curtailed sampling, simple      147
Curtailed sampling, symmetric      151
Delta method      228
Discrete time problem      116
Dominated Convergence Theorem      197
Double minimax property      71
Double sampling      173
Double sampling plan      3
Double sampling procedure      167
Double triangular tests      242 243
Double-blind clinical trial      248 254
Dynamic programming      115
Dynamic programming equation      112
Dynamic programming method      111
E-M algorithm      247
Edgeworth expansion      172
Effective coverage probability      253
Effective level of significance      247 249 250 256
Effective power      249 251 260
Efficiency of the SPRT      99 100
Efficient score      240
Empirical distribution function      123 128 131
Empirical distribution functions      216 287
Error probabilities      2 9 16 24 40 45 46 48 49 58 71 73 83 88 90 97 99 124 125 174 247
Error rates      51 see
Estimable      149
Euler — Maclaurin sum formula      78
Excess over the boundary      86 94
Expected sample number      17
Expected sample size      2 27 99 211 see
Expected stopping time      35
Expected time      49
Exponential distribution      44
Exponential family      11 144 145 177
Exponential family of densities      237
Exponential survival curves      85
Extremum      187
Family of densities      14
Finite sure termination      70
Fisher information      240
Fixed-sample procedure      5
Fixed-sample procedures      17 18
Fixed-sample size procedure      90 99 152 158 201
Fixed-sample size test (FSST)      74
Fixed-Size confidence bounds      203
Fixed-width confidence interval      246 252
Fixed-width confidence intervals      191

Fixed-width confidence intervals, large-sample      196
Fixed-width estimation      234
Fixed-width interval      158
Fundamental identity      30
Generalized likelihood ratio tests      86 88
Generalized probability ratio test (GPRT)      173
Generating distributions      290
Glivenko — Cantelli theorem      123
Govindarajulu — Howard approximation      73
Group sequential sampling      111
Grouped rank tests      127
Hall's sequential test      279
Helmert's transformation      61 188
Highest reachable point      113
Hypergeometric distribution      237
Hypothesis of symmetry      126
Hypothesis-testing problem      11
Impossible point      146
Indifference zone      27
Inequalities for error probabilities      16
Infinitesimal surface element      59
Initial sample size      1
Inner acceptance boundary      134 135
intercept      271
Intercepts      13
Interchange of integration and summation      155
Interchange of summation and expectation      23
Interim stage      246
Interval of convergence      149
Invariance considerations      79
Invariant sufficiency      127
Inverse binomial sampling      151
Inverse function      123
Inversion formula for an integral      78
iterations      227
Jump discontinuity      130
Khintchine's theorem      80
Koopman — Darmois families      86 88
Kronecker's delta      50
l'Hospital's rule      20
Lachin's formula      256
Laplace distribution      125
Laplace's method      78
Large-sample properties      79
Large-sample sequential test      85
Law of the iterated logarithm      122
Least squares estimate      204
Lehmann alternatives      127
Lethal dose      229
level of significance      11
Likelihood ratio      127
Likelihood ratio open-ended test      89
Linear hypothesis-testing problem      75
Log likelihood      240
Log rank statistic      240
Logistic distribution function      58
Lower boundary      93
Lower bounds for the ASN      33
Lower confidence limit      179
Lower stopping bound      46
m-dimensional Euclidean space      2
Mann — Whitney statistic      216
Mantel — Haenszel statistic      238
Mantel — Haenszel test      240 264
MATLAB      265
Maximum ASN      102
Maximum likelihood estimate (mle)      185 240
Maximum Likelihood Estimation      191
Maximum likelihood SPRT      81
Mean      6
Means procedure      219
Measure theory      196
Median      126
Method of maximum likelihood      247
Method of weight functions      59 79
Mill's ratio      49
minimax      152
Minimax solution (MMS)      166
Minimum probability ratio test (MPRT)      74
Minimum variance unbiased estimate      216
MLE      232
Modified likelihood ratio      62
Modified likelihoods      60
Modified rank order SPRT      132
Modified SPRT      49
Moment-generating function      22 149
Moments of N      21
Monotone likelihood ratio (MLR)      46 173 176
Monotonicity of the power function      46
Monotonicity property      46
Monte Carlo results      202
Monte Carlo studies      121 127 215
Most powerful fixed-sample procedure      100
Most powerful test      11 126
Natural parameter space      89
Newton — Raphson algorithm      78
Nominal error probability      16
Nominal level of significance      260
Nominal power      260
Non-linear unbiased estimates      204
Nonparametric confidence intervals, p-point of a distribution function      210
Normal response      247
Nuisance parameter      59 75 79 81 170 191 240
OC and ASN functions of T      74
OC function      32 36 44 55 56 83 85 93 98
OC function, monotonicity      103
OC function, symmetry      103
One-sided alternative      8
Open-ended tests      86 88
Operating characteristic (OC)      2
Operating characteristic (OC) curve      20
Operating characteristic (OC) function      19 47
Optimal properties of SPRT      44
Optimal sequential procedure      2
Optimum fixed-sample size test      99 102 105
Optimum property of the SPRT      102 106
Optimum property of Wald's SPRT      46
Optimum SPRT      59
Optimum test procedure      110
Overshoot      246
Percentage error      173
Perfect information      114
Pitman-efficiencies      215
Positive drift      86
Posterior probability      107
Power curve of the SPRT      53
Power function      58
Power of the SPRT      53
Power of the test      6
Predetermined alternative      247
Prior distribution      59
Probability of absorption      49
Probability of type I error      53
Properties of sequential t-test      70
Properties of the SPRT      61
Property M      46
Proportional accuracy      200
Radon — Nikodym derivative      214
Random sample size      25
Random walk      36 44 82
Randomized design      254
RANGE      187
Rank order      127 130
Rank order SPRT      287
Rank sum test      127
Rank test procedure      123
Rao — Blackwell theorem      146
Regression coefficients      203
Regularity assumptions      211
Rejection boundary      133

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