Sequential Statistical Procedures

PrefaceNotationChapter 1 Introduction and Certain Double Sampling Procedures 1.1 Introduction to Sequential Testing 1.2 Sampling Inspection 1.3 Loss and Risk Functions 1.4 Certain Double Sampling ProceduresChapter 2 The Sequential Probability Ratio 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 SPRT 2.7 Formulas for Calculating the Operating Characteristic and the 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 SPRTsChapter 3 Sequential Tests for Composite Hypotheses 3.1 Wald’s (1947) Method of Weight Functions 3.2 Sequential t- and t2-Tests and Sequential Analogues of Stein’s Two-Stage Test 3.3 Sequential F-Test 3.4 Certain Two-Sample Sequential Procedures 3.5 Fraser Sufficiency and Conditional Test 3.6 Invariant Sequential Procedures 3.7 Sequential Likelihood Ratio Test Procedures 3.8 Sequential Tests between Three Hypotheses 3.9 Sequential k-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 Application 3.14 Certain Nonparametric Sequential Test Procedures 3.15 Locally Most Powerful (LMP) Sequential TestsChapter 4 Sequential Estimation 4.1 Introductory Remarks 4.2 Certain Two-Stage Procedures 4.3 Formulation of the Problem of Sequential Estimation by Intervals or Sets 4.4 Wald’s Sequential Estimation Procedures 4.5 Certain General Concepts of Sequential Estimation 4.6 Cramer-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 Estimation Procedure Is Nonsequential 4.10 Sequential Estimation and Certain Closed Sequential Decision Procedures 4.11 Estimation by Double Sampling 4.12 Large Sample Theory of Sequential Estimation 4.13 Sequential Confidence Intervals for the Mean of a Normal Population with Unknown Variance 4.14 The Asymptotic Theory of Fixed-Width Sequential Confidence Intervals for the Mean 4.15 Asymptotic Theory of Fixed-Size Sequential Confidence Bounds for Linear Regression Parameters 4.16 Confidence Sequences for Other Parameters 4.17 Sequential Estimation of the Mean Vector of a Multivariate Normal Distribution 4.18 A General Method of Determining Fixed-Width Confidence Intervals 4.19 Sequential Estimation of the Size of a Finite Population 4.20 Consistency of Certain Sequential Estimators 4.21 Asymptotically Optimal Bayes Sequential Estimation 4.22 Sequential Nonparametric Confidence Intervals for Certain Parameters of the Population 4.23 Certain Problems of Optimal StoppingAppendix 1 Solution to Wald's EquationAppendix 2 Differentiation of an ExpectationAppendix 3 On the Moments of a Random VariableAppendix 4 The Normal Diffusion ProcessAppendix 5 Large Sample Properties of Maximum Likelihood EstimatesAppendix 6 A Table of Standard DistributionsAppendix 7 A Useful Convergence Theorem of CramerAppendix 8 Backward InductionReferences and Author IndexSubject Index