The Foundations of Statistics

Front Cover
Courier Corporation, Jun 1, 1972 - Mathematics - 310 pages
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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.
 

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Contents

Postulates of a personalistic theory of decision
1
PERSONAL PROBABILITY
28
OBSERVATION
47
CRITICAL COMMENTS ON PERSONAL PROBABILITY
58
UTILITY
72
Small worlds
83
Historical and critical comments on utility
93
10
100
Randomization
216
Mixed acts in statistics
217
POINT ESTIMATION 1 Introduction
220
27
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
30
241

PARTITION PROBLEMS
120
13
132
17
139
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
Sequential probability ratio procedures
215
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
40
280
BIBLIOGRAPHIC SUPPLEMENT
283
TECHNICAL SYMBOLS
299
AUTHOR INDEX
301
GENERAL INDEX
305
46
306
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