Sequential Statistical Procedures

Sequential Statistical Procedures

1st Edition - January 1, 1975

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  • Author: Z. Govindarajulu
  • eBook ISBN: 9781483263328

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Probability and Mathematical Statistics, Volume 26: Sequential Statistical Procedures provides information pertinent to the sequential procedures that are concerned with statistical analysis of data. This book discusses the fundamental aspects of sequential estimation. Organized into four chapters, this volume begins with an overview of the essential feature of sequential procedure. This text then examines the sequential probability ratio test procedure and provides a method of constructing a most powerful test for a simple hypothesis versus simple alternative-testing problem. Other chapters consider the problem of testing a composite hypothesis against a composite alternative. This book discusses as well the theory of sequential tests that is appropriate for distinguishing between two simple or composite hypotheses. The final chapter deals with the theory of sequential estimation. This book is a valuable resource for graduate students, research workers, and users of sequential procedures.

Table of Contents

  • Preface


    Chapter 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 Procedures

    Chapter 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 SPRTs

    Chapter 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 Tests

    Chapter 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 Stopping

    Appendix 1 Solution to Wald's Equation

    Appendix 2 Differentiation of an Expectation

    Appendix 3 On the Moments of a Random Variable

    Appendix 4 The Normal Diffusion Process

    Appendix 5 Large Sample Properties of Maximum Likelihood Estimates

    Appendix 6 A Table of Standard Distributions

    Appendix 7 A Useful Convergence Theorem of Cramer

    Appendix 8 Backward Induction

    References and Author Index

    Subject Index

Product details

  • No. of pages: 584
  • Language: English
  • Copyright: © Academic Press 1975
  • Published: January 1, 1975
  • Imprint: Academic Press
  • eBook ISBN: 9781483263328

About the Author

Z. Govindarajulu

About the Editors

Z. W. Birnbaum

E. Lukacs

Affiliations and Expertise

Bowling Green State University

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