Sequential Analysis

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Courier Corporation, Jun 10, 2004 - Mathematics - 212 pages
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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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Contents

INTRODUCTION
1
SEQUENTIAL TEST OF A STATISTICAL
22
Chapter S THE SEQUENTIAL PROBABILITY RATIO TEST
37
OUTLINE OF A THEORY OF SEQUENTIAL
70
APPLICATION OF THE GENERAL THEORY
88
TESTING THE DIFFERENCE BETWEEN
106
DISTRIBUTION WITH KNOWN STANDARD DEVIATION
117
Chapter S TESTING THAT THE STANDARD DEVIATION
125
THE PROBLEM OF SEQUENTIAL ESTIMATION
151
APPENDIX
157
Upper and Lower Limits for the ASN Function of a Sequential
170
Derivation of Exact Formulas for the OC and ASN Functions
181
Approximate Distribution of n When z Is Normally Distributed
191
EFFICIENCY or THE SEQUENTIAL PROBABILITY RATIO TEST
196
DETERMINATION OF OPTIMUM WEIGHT FUNCTIONS wa6 AND wr6
203
INDEX
209

TESTING THAT THE MEAN OF A NORMAL
134

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