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Sequential Analysis.

Author: Abraham Wald
Publisher: Dover Publications, 2013.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
In 1943, while in charge of Columbia University's Statistical Research Group, Abraham Wald devised Sequential Design, an innovative statistical inference system. Because the decision to terminate an experiment is not predetermined, sequential analysis can arrive at a decision much sooner and with substantially fewer observations than equally reliable test procedures based on a predetermined number of observations.  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Abraham Wald
ISBN: 130632856X 9781306328562 9780486783239 0486783235
OCLC Number: 868280879
Description: 1 online resource
Contents: Cover Page; Title Page; Copyright Page; Contents; Introduction; Part I. General Theory; Chapter 1. Elements of the Current Theory of Testing Statistical Hypotheses; 1.1 Random Variables and Probability Distributions; 1.1.1 Notion of a Random Variable; 1.1.2 Cumulative Distribution Function (c.d.f.) of a Random Variable; 1.1.3 Probability Density Function; 1.1.4 Discrete Random Variables; 1.1.5 Expected Value and Higher Moments of a Random Variable .; 1.2 Notion of A Statistical Hypothesis; 1.2.1 Unknown Parameters of a Distribution; 1.2.2 Simple and Composite Hypotheses. 1.3 Outline of the Current Procedure for Testing Statistical Hypotheses1.3.1 The Sample; 1.3.2 The General Nature of a Test Procedure; 1.3.3 Principles for Choosing a Critical Region; 1.3.4 Number of Observations Necessary if <U+00dc> and <U+00dd> Have Preassigned Values; 1.3.5 Testing a Hypothesis Viewed as a Decision between Two Courses of Action; Chapter 2. Sequential Test of A Statistical Hypothesis: General Discussion; 2.1 Notion Of A Sequential Test; 2.2 Consequences Of the Choice of Any Particular Sequential Test; 2.2.1 The Operating Characteristic Function. 2.2.2 The Average (Expected) Sample Number (ASN) Function of a Sequential Test2.3 Principles for the Selection of A Sequential Test; 2.3.1 Degree of Preference for Acceptance or Rejection of the Null Hypothesis H0 as a Function of the Parameter <U+006b>; 2.3.2 Requirements Imposed on the OC Function; 2.3.3 The ASN Function as a Basis for the Selection of a Sequential Test; 2.4 The Case When A Simple Hypothesis H0 is Tested Against A Single Alternative H1; 2.4.1 Efficiency of a Sequential Test; 2.4.2 Efficiency of the Current Test Procedure, Viewed as a Particular Case of a Sequential Test. Chapter 3. The Sequential Probability Ratio Test for Testing A Simple Hypothesis H0 Against A Single Alternative H13.1 Definition of the Sequential Probability Ratio Test; 3.2 Fundamental Relations Among the Quantities <U+00dc>, <U+00dd>, A, and B; 3.3 Determination of the Constants A and B in Practice; 3.4 The OC Function of the Sequential Probability Ratio Test; 3.5 The ASN Function of A Sequential Probability Ratio Test; 3.6 Saving in the Number of Observations Effected by the Use of the Sequential Probability Ratio Test Instead of the Current Test Procedure. 3.7 Lower Limit of the Probability that the Sequential Test Will Terminate with A Number of Trials Less than or Equal to A Given Number3.8 Truncation of the Sequential Test Procedure; 3.9 Increase in The Expected Number of Observations Caused by Replacing the Exact Values A (<U+00dc>, <U+00dd>) and B(<U+00dc>, <U+00dd>) by (1 --
<U+00dd>)/<U+00dc> and <U+00dd>/(1 --
<U+00dc>), Respectively; Chapter 4. Outline of A Theory of Sequential Tests of Simple and Composite Hypotheses Against A Set of Alternatives; 4.1 Tests of Simple Hypotheses; 4.1.1 Introductory Remarks; 4.1.2 Test of a Simple Hypothesis against One-Sided Alternatives.

Abstract:

In 1943, while in charge of Columbia University's Statistical Research Group, Abraham Wald devised Sequential Design, an innovative statistical inference system. Because the decision to terminate an experiment is not predetermined, sequential analysis can arrive at a decision much sooner and with substantially fewer observations than equally reliable test procedures based on a predetermined number of observations. The system's immense value was immediately recognized, and its use was restricted to wartime research and procedures. In 1945, it was released to the public and has since revolutionized many aspects of statistical practice. This book is Professor Wald's own description of the system. Part I contains a discussion of the general theory of the sequential probability ratio test, with comparisons to traditional statistical inference systems. Part II discusses applications that illustrate the general theory and raise points of theoretical interest specific to these applications. Part III outlines a possible approach to the problem of sequential multi-valued decisions and estimation. All three sections can be understood by readers with only a background in college algebra and a first course in calculus. Mathematical derivations of somewhat intricate nature appear in the appendix. Sequential Analysis offers statistical researchers a time- and money-saving approach, introduces students to one of the major systems in contemporary use, and presents those already acquainted with the system with valuable background information.

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