# The Foundations of Statistics

Courier Corporation, Jun 1, 1972 - Mathematics - 310 pages
Classic analysis of the foundations of statistics and development of personal probability, one of the greatest controversies in modern statistical thought. Revised edition. Calculus, probability, statistics, and Boolean algebra are recommended.

### Contents

 Postulates of a personalistic theory of decision 1 Consequences acts and decisions 10 The simple ordering of acts with respect to preference 17 PERSONAL PROBABILITY 28 OBSERVATION 47 CRITICAL COMMENTS ON PERSONAL PROBABILITY 58 UTILITY 72 Small worlds 83
 Sequential probability ratio procedures 215 Randomization 216 Mixed acts in statistics 217 POINT ESTIMATION 1 Introduction 220 The verbalistic concept of point estimation 221 Criteria that have been proposed for point estimates 223 A behavioralistic review of the criteria for point estimation 229 A behavioralistic review continued 234

 Historical and critical comments on utility 93 PARTITION PROBLEMS 120 STATISTICS PROPER 154 A PERSONALISTIC REINTERPRETATION OF THE MINIMAX THEORY 172 THE PARALLELISM BETWEEN THE MINIMAX THEORY AND THE THEORY 178 THE MATHEMATICS OF MINIMAX PROBLEMS 184 Bilinear games 186 An example of a bilinear game 189 Bilinear games exhibiting symmetry 193 OBJECTIONS TO THE MINIMAX RULES 1 Introduction 200 Utility and the minimax rule 201 Almost subminimax acts 203 The minimax rule does not generate a simple ordering 205 THE MINIMAX THEORY APPLIED TO OBSERVATIONS 1 Introduction 208 Sufficient statistics 212 The approach to certainty 214
 A behavioralistic review concluded 244 TESTING 1 Introduction 246 A theory of testing 247 Testing in practice 252 INTERVAL ESTIMATION AND RELATED TOPICS 1 Estimates of the accuracy of estimates 257 Interval estimation and confidence intervals 259 Tolerance intervals 262 EXPECTED VALUE 263 CONVEX FUNCTIONS 266 BIBLIOGRAPHIC MATERIAL 270 BIBLIOGRAPHIC SUPPLEMENT 283 TECHNICAL SYMBOLS 299 AUTHOR INDEX 301 GENERAL INDEX 305 Copyright

### References to this book

 Selected Papers of Hirotugu AkaikeLimited preview - 1998
 Theoretical StatisticsLimited preview - 1979
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