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Front Cover; Sequential Statistical Procedures; Copyright Page; Dedication; Table of Contents; Preface; Notation; CHAPTER 1. Introduction and Certain DoubleSampling Procedures; 1.1 Introduction to Sequential Testing; 1.2 Sampling Inspection; 1.3 Loss and Risk Functions; 1.4 Certain Double Sampling Procedures; CHAPTER 2. The Sequential ProbabilityRatio Test; 2.1 The Sequential Probability Ratio Test (SPRT); 2.2 Finite Termination of the SPRT; 2.3 The Operating Characteristic Function(OC Function); 2.4 Average Sample Number; 2.5 Wald's Fundamental Identity
2.6 Bounds for the Expected Sample Size in a SPRT2.7 Formulas for Calculating the Operating Characteristic andthe Average Sample Number of Some Sequential Tests; 2.8 Truncated SPRT; 2.9 Optimal Properties of the SPRT; 2.10 Generalized SPRT (GSPRT); 2.11 Restricted SPRT; 2.12 Extended SPRTs; 2.13 Asymptotic Properties of SPRTs; CHAPTER 3. Sequential Tests for CompositeHypotheses; 3.1 Wald's (1947) Method of Weight Functions; 3.2 Sequential t- and t2- Tests and SequentialAnalogues of Stein's Two-Stage Test; 3.3 Sequential F-Test; 3.4 Certain Two-Sample Sequential Procedures
3.5 Fraser Sufficiency and Conditional Tests3.6 Invariant Sequential Procedures; 3.7 Sequential Likelihood Ratio Test Procedures; 3.8 Sequential Tests Between Three Hypotheses; 3.9 Sequentialk-Decision Problems; 3.10 Sequential Tests for Two-Sided Alternatives; 3.11 Efficiency of the SPRT; 3.12 Bayes Sequential Procedures; 3.13 Iterated Logarithm Inequalities and Their Applicationto Sequential Testing Hypotheses; 3.14 Certain Nonparametric Sequential Test Procedures; 3.15 Locally Most Powerful (LMP) Sequential Tests; CHAPTER 4. Sequential Estimation; 4.1 Introductory Remarks
4.2 Certain Two-Stage Procedures4.3 Formulation of the Problem of Sequential Estimationby Intervals or Sets; 4.4 Wald's Sequential Estimation Procedures; 4.5 Certain General Concepts of Sequential Estimation; 4.6 Cramér-Rao Lower Bound for the Sequential Case; 4.7 Sufficiency and Completeness in the Sequential Case; 4.8 Minimax Estimation; 4.9 A Class of Situations Where Bayes Sequential EstimationProcedure Is Nonsequential; 4.10 Sequential Estimation and Certain Closed Sequential DecisionProcedures; 4.11 Estimation by Double Sampling; 4.12 Large Sample Theory of Sequential Estimation
4.13 Sequential Confidence Intervals for the Mean of a NormalPopulation with Unknown Variance4.14 The Asymptotic Theory of Fixed-Width Sequential ConfidenceIntervals for the Mean; 4.15 Asymptotic Theory of Fixed-Size Sequential Confidence Boundsfor Linear Regression Parameters; 4.16 Confidence Sequences for Other Parameters; 4.17 Sequential Estimation of the Mean Vector of a MultivariateNormal Distribtuion; 4.18 A General Method of Determining Fixed-WidthConfidence Intervals; 4.19 Sequential Estimation of the Size of a Finite Population; 4.20 Consistency of Certain Sequential Estimators
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Includes bibliographical references (pages 537-553).
Probability and mathematical statistics ; v. 26