Govindarajulu Z. Sequential statistics

Singapore: World Scientific, 2004. - 335p.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.Introduction to Sequential Procedures
Sample Size Distribution
Stein's Two-stage Procedure
The ProcedureThe Sequential Probability Ratio Test (SPRT)
SPRT: It's Finite Termination and Bounds
The Operating Characteristic Function
The Average Sample Number
Wald's Fundamental Identity
Applications of the Fundamental Identity
Bounds for the Average Sample Number
The OC Function
The Average Sample Number
Truncated SPRT
Optimal Properties of the SPRT
The Restricted SPRT
Large-Sample Properties of the SPRT
ProblemsMethod of Weight Functions
Sequential Chi-square Test
Sequential t and t Tests
Uniform Asymptotic Expansion and Inversion for an Integral
Simulation Studies
Asymptotic Normality of the Statistic T
Finite Sure Termination of Sequential t- and t-tests
Sequential t-test (or t-test for Two-sided Alternatives)
The Sequential Test T
An Alternative Sequential Test T'
Sequential F-test
Inversion Formula
Likelihood Ratio Test Procedures
Generalized Likelihood Ratio Tests for Koopman-Darmois Families
Armitage-Sobel-Wald Test
OC Function
Bounds for ASN
Testing Two-sided Alternatives for Normal Mean
Efficiency of the SPRT Relative to the Fixed-Sample Size Procedure at the Hypotheses
Relative Efficiency at
Limiting Relative Efficiency of the SPRT
Bayes Sequential Binomial SPRT
The Methods of Calculation
Dynamic Programming Method for the Binomial Case
The Dynamic Programming Equation
Bayes Sequential Procedures for the Normal Mean
Small Error Probability and Power One Test
Tests with small error probability
Tests with Power One
Kolmogorov-Smirnov Tests with Power One
Sequential Sign Test
Rank Order SPRT's Based on Lehmann Alternatives: Two-Sample Case
One-Sample Rank Order SPRT's for Symmetry
One-sided Alternatives
Two-sided Alternatives
Appendix: A Useful Lemma
ProblemsBasic Concepts
Sufficiency and Completeness
Cramer-Rao Lower Bound
Stein's Procedure for Estimating the Mean of a Normal Distribution with Unknown Variance
Normal Populations
Procedures for Estimating the Common Mean
A Simpler Estimator
Double-Sampling Estimation Procedures
Estimation with given Variance: Single unknown Parameter
Estimation in the presence of a Nuisance Parameter
Confidence Intervals
Fixed Length Confidence Intervals Based on SPRT
kth step
Applications
Special Case
Large-Sample Theory for Estimators
Special Cases
Determination of Fixed-width Intervals
Interval Estimation for the Mean
Risk-efficient Estimation of the Mean
Fixed-Size Confidence Bounds
When is Unknown
Asymptotic Properties of the Class C
Confidence Intervals for P(X)