Details

Autor(en) / Beteiligte

• Ghosh, Malay
• Mukhopadhyay, Nitis,
• Sen, Pranab Kumar,

Titel

Sequential estimation

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliographical references and indexes.
• Sequential Estimation; Contents; Preface; 1. Introduction and Coverage; 1.1 Introduction; 1.2 Some Sequential Sampling Schemes in Practice; 1.2.1 Binomial Waiting-Time Distribution; 1.2.2 Hypergeometric Waiting-Time Distribution; 1.2.3 Capture-Mark-Recapture Procedures; 1.2.4 Time-Sequential Models; 1.2.5 Sequential Models in Reliability Problems; 1.2.6 Recursive Estimation and Sequential Schemes; 1.3 Organization of This Book; 2. Probabilistic Results in Sequential Analysis; 2.1 Introduction; 2.2 Martingales; 2.3 Stopping Times; 2.4 Martingale Inequalities and Identities
• 2.5 Submartingale Convergence Theorems2.6 Martingale Central Limit Theorems; 2.7 Random Central Limit Theorems and Berry-Esseen Bounds; 2.8 Renewal Theorem-First Passage and Residual Waiting Times; 2.9 Nonlinear Renewal Theory; 2.10 Exercises; 3. Some Basic Concepts for Fixed-Sample Estimation; 3.1 Introduction; 3.2 Decision-Theoretic Notions; 3.3 Bayesian Decision Rules; 3.4 Sufficiency and Efficiency; 3.5 Invariance and Transitivity; 3.6 Method of Maximum Likelihood; 3.7 Why Sequential?; 3.8 Exercises; 4. General Aspects of Sequential Estimation; 4.1 Introduction
• 4.2 Sufficiency, Rao-Blackwell Theorem, and Transitivity4.3 Cramér-Rao and Related Inequalities; 4.4 Sequential Binomial Sampling Plans; 4.5 Exercises; 5. Sequential Bayesian Estimation; 5.1 Introduction; 5.2 Bayesian Sequential Decision Rules; 5.3 Sequential Bayesian Estimation; 5.4 Asymptotically Pointwise Optimal (APO) Stopping Rules; 5.5 Hierarchical and Empirical Bayes Sequential Estimation; 5.6 Exercises; 6. Multistage Estimation; 6.1 Introduction; 6.2 Fixed-Width Confidence Intervals and Two-Stage Procedures; 6.2.1 Stein's Two-Stage Procedure; 6.2.2 Modified Two-Stage Procedure
• 6.2.3 Further Generalizations6.3 Fixed-Width Confidence Intervals and Three-Stage Procedures; 6.3.1 The Global Theory; 6.3.2 Applications of the Three-Stage Procedure; 6.4 Fixed-Width Confidence Intervals and Accelerated Sequential Procedures; 6.4.1 The Global Theory; 6.5 Point Estimation Problems; 6.5.1 Minimum Risk Normal Mean Problem; 6.5.2 Two-Stage Procedure; 6.5.3 Modified Two-Stage Procedure; 6.5.4 Three-Stage Procedure; 6.5.5 Accelerated Sequential Procedure; 6.6 Other Related Estimation Problems; 6.6.1 Point Estimation in Exponential Populations; 6.6.2 Estimation of Normal Variance
• 6.6.3 Binomial and Negative Binomial Problems6.7 Comparison of Populations; 6.7.1 Fixed-Width Confidence Intervals; 6.7.2 Point Estimation; 6.8 Estimation in Multivariate Normal and Linear Models; 6.8.1 Estimation of Mean Vector When Σ Is Arbitrary; 6.8.2 Comparison of Populations; 6.8.3 Linear Regression Problems; 6.8.4 Shrinkage Estimators; 6.8.5 Estimation of Ordered Parameters; 6.9 Exercises; 7. Parametric Sequential Point Estimation; 7.1 Introduction; 7.2 Estimation of the Normal Mean; 7.3 Estimation of the Difference of Two Normal Means; 7.4 Point Estimation in Linear Models
• 7.5 Estimation of the Multivariate Normal Mean
• The only comprehensive guide to the theory and practice of one of today's most important probabilistic techniquesThe past 15 years have witnessed many significant advances in sequential estimation, especially in the areas of three-stage and nonparametric methodology. Yet, until now, there were no references devoted exclusively to this rapidly growing statistical field.Sequential Estimation is the first, single-source guide to the theory and practice of both classical and modern sequential estimation techniques--including parametric and nonparametric methods. Researchers in sequ
• English