Sequential estimation

Cover......Page 1
Title......Page 5
Contents......Page 9
Preface......Page 15
1.1 Introduction......Page 17
1.2 Some Sequential Sampling Schemes in Practice......Page 23
1.2.2 Hypergeometric Waiting-Time Distribution......Page 24
1.2.3 Capture-Mark-Recapture Procedures......Page 25
1.2.4 Time-Sequential Models......Page 26
1.2.5 Sequential Models in Reliability Problems......Page 27
1.3 Organization of This Book......Page 28
2.2 Martingales......Page 35
2.3 Stopping Times......Page 37
2.4 Martingale Inequalities and Identities......Page 40
2.5 Submartingale Convergence Theorems......Page 51
2.6 Martingale Central Limit Theorems......Page 56
2.7 Random Central Limit Theorems and Berry-Esseen Bounds......Page 60
2.8 Renewal Theorem First Passage and Residual Waiting Times......Page 66
2.9 Nonlinear Renewal Theory......Page 74
2.10 Exercises......Page 81
3.2 Decision-Theoretic Notions......Page 85
3.3 Bayesian Decision Rules......Page 89
3.4 Sufficiency and Efficiency......Page 91
3.5 Invariance and Transitivity......Page 97
3.6 Method of Maximum Likelihood......Page 98
3.7 Why Sequential?......Page 100
3.8 Exercises......Page 101
4.1 Introduction......Page 105
4.2 Sufficiency, Rao-Blackwell Theorem, and Transitivity......Page 106
4.3 Cramr-Rao and Related Inequalities......Page 112
4.4 Sequential Binomial Sampling Plans......Page 117
4.5 Exercises......Page 123
5.1 Introduction......Page 127
5.2 Bayesian Sequential Decision Rules......Page 128
5.3 Sequential Bayesian Estimation......Page 138
5.4 Asymptotically Pointwise Optimal (APO) Stopping Rules......Page 141
5.5 Hierarchical and Empirical Bayes Sequential Estimation......Page 154
5.6 Exercises......Page 166
6.2 Fixed-Width Confidence Intervals and Two-Stage Procedures......Page 169
6.2.1 Stein\'s Two-Stage Procedure......Page 170
6.2.2 Modified Two-Stage Procedure......Page 172
6.2.3 Further Generalizations......Page 173
6.3 Fixed-Width Confidence Intervals and Three-Stage Procedures......Page 175
6.3.1 The Global Theory......Page 176
6.3.2 Applications of the Three-Stage Procedure......Page 180
6.4 Fixed-Width Confidence Intervals and Accelerated Sequential Procedures......Page 184
6.4.1 The Global Theory......Page 185
6.5.1 Minimum Risk Normal Mean Problem......Page 189
6.5.2 Two-Stage Procedure......Page 190
6.5.4 Three-Stage Procedure......Page 191
6.5.5 Accelerated Sequential Procedure......Page 193
6.6.1 Point Estimation in Exponential Populations......Page 194
6.6.2 Estimation of Normal Variance......Page 198
6.6.3 Binomial and Negative Binomial Problems......Page 200
6.7.1 Fixed-Width Confidence Intervals......Page 201
6.7.2 Point Estimation......Page 204
6.8 Estimation in Multivariate Normal and Linear Models......Page 207
6.8.1 Estimation of Mean Vecior When S Is Arbitrary ......Page 208
6.8.3 Linear Regression Problems......Page 213
6.8.4 Shrinkage Estimators......Page 218
6.8.5 Estimation of Ordered Parameters......Page 219
6.9 Exercises......Page 220
7.1 Introduction......Page 227
7.2 Estimation of the Normal Mean......Page 228
7.3 Estimation of the Difference of Two Normal Means......Page 238
7.4 Point Estimation in Linear Models......Page 240
7.5 Estimation of the Multivariate Normal Mean......Page 243
7.6 Sequential Shrinkage Estimation......Page 248
7.7 Sequential Estimation of the Gamma Scale Parameter......Page 256
7.8 Exercises......Page 259
8.2 Fixed-Width Interval Estimation of the Normal Mean......Page 265
8.3 Sequential Interval Estimation of the Difference of Two Normal Means......Page 272
8.4 Fixed-Size Confidence Bounds for Linear Regression Parameters......Page 276
8.5 Confidence Region for the Mean Vector......Page 279
8.6 Exercises......Page 281
9.1 Introduction......Page 285
9.2 Estimable Parameters and MRE......Page 286
9.3 Differentiable Statistical Functionals and MRE......Page 303
9.4 Simple Semiparametric Models......Page 309
9.5 Multiparameter AMRE, I......Page 319
9.6 Multiparameter AMRE, II......Page 325
9.7 Exercises......Page 328
10.1 Introduction......Page 331
10.2 Type-A Confidence Intervals......Page 332
10.3 Type-B Confidence Intervals......Page 339
10.4 Nonparametric Confidence Sets......Page 344
10.5 Exercises......Page 348
11.2 Bias and Confidence Interval Evaluations......Page 351
11.2.1 Unknown Variance Case......Page 354
11.2.2 Another Practical Approach......Page 355
11.3 Sequential x2 and F Tests......Page 356
11.4 Exercises......Page 357
12.1 Introduction......Page 359
12.2 Time-Sequential Estimation for Poisson and Wiener Processes......Page 361
12.3 Time-Sequential Estimation for Exponential Life-Testing Models......Page 366
12.4 Some Generalizations......Page 375
12.5 Exercises......Page 380
13.1 Introduction......Page 383
13.2 Bundle Strength of Filaments......Page 384
13.3 System Reliability and Availability......Page 393
13.4 Sequential Estimation of Functional Parameters......Page 399
13.5 Exercises......Page 406
14.1 Introduction......Page 409
14.2 The CMRR and Two-Sample Estimators of N......Page 410
14.3 The CMRR and Multisample Estimators of N......Page 413
14.4 Estimation of N Under Inverse Sampling Schemes......Page 421
14.5 Sequential Tagging Schemes......Page 423
14.6 Bounded Percentage Width Confidence Interval for N......Page 428
14.7 Asymptotically Optimal Sequential Point Estimation of N......Page 434
14.8 Exercises......Page 437
15.1 Introduction......Page 441
15.2 General Asymptotics......Page 442
15.3 Sequential Perspectives......Page 447
15.4 Exercises......Page 459
References......Page 461
Author Index......Page 485
Subject Index......Page 489