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Sequential Analysis

Tests and Confidence Intervals

  • Book
  • © 1985

Overview

Authors:
  1. David Siegmund

    1. Department of Statistics, Stanford University, Stanford, USA

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Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction and Examples

    • David Siegmund
    Pages 1-7

  3. The Sequential Probability Ratio Test

    • David Siegmund
    Pages 8-33

  4. Brownian Approximations and Truncated Tests

    • David Siegmund
    Pages 34-69

  5. Tests with Curved Stopping Boundaries

    • David Siegmund
    Pages 70-104

  6. Examples of Repeated Significance Tests

    • David Siegmund
    Pages 105-140

  7. Allocation of Treatments

    • David Siegmund
    Pages 141-154

  8. Interval Estimation of Prescribed Accuracy

    • David Siegmund
    Pages 155-164

  9. Random Walk and Renewal Theory

    • David Siegmund
    Pages 165-187

  10. Nonlinear Renewal Theory

    • David Siegmund
    Pages 188-212

  11. Corrected Brownian Approximations

    • David Siegmund
    Pages 213-228

  12. Miscellaneous Boundary Crossing Problems

    • David Siegmund
    Pages 229-240

  13. Back Matter

    Pages 241-274
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Keywords

About this book

The modern theory of Sequential Analysis came into existence simultaneously in the United States and Great Britain in response to demands for more efficient sampling inspection procedures during World War II. The develop­ ments were admirably summarized by their principal architect, A. Wald, in his book Sequential Analysis (1947). In spite of the extraordinary accomplishments of this period, there remained some dissatisfaction with the sequential probability ratio test and Wald's analysis of it. (i) The open-ended continuation region with the concomitant possibility of taking an arbitrarily large number of observations seems intol­ erable in practice. (ii) Wald's elegant approximations based on "neglecting the excess" of the log likelihood ratio over the stopping boundaries are not especially accurate and do not allow one to study the effect oftaking observa­ tions in groups rather than one at a time. (iii) The beautiful optimality property of the sequential probability ratio test applies only to the artificial problem of testing a simple hypothesis against a simple alternative. In response to these issues and to new motivation from the direction of controlled clinical trials numerous modifications of the sequential probability ratio test were proposed and their properties studied-often by simulation or lengthy numerical computation. (A notable exception is Anderson, 1960; see III.7.) In the past decade it has become possible to give a more complete theoretical analysis of many of the proposals and hence to understand them better.

Authors and Affiliations

  • Department of Statistics, Stanford University, Stanford, USA

    David Siegmund

Bibliographic Information

  • Book Title: Sequential Analysis

  • Book Subtitle: Tests and Confidence Intervals

  • Authors: David Siegmund

  • Series Title: Springer Series in Statistics

  • DOI: https://doi.org/10.1007/978-1-4757-1862-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1985

  • Hardcover ISBN: 978-0-387-96134-7Published: 07 August 1985

  • Softcover ISBN: 978-1-4419-3075-0Published: 01 December 2010

  • eBook ISBN: 978-1-4757-1862-1Published: 09 April 2013

  • Series ISSN: 0172-7397

  • Series E-ISSN: 2197-568X

  • Edition Number: 1

  • Number of Pages: XI, 274

  • Topics: Statistical Theory and Methods, Probability Theory and Stochastic Processes

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