Ferguson T. Mathematical Statistics. A Decision Theoretic Approach 1967

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Ferguson T. Mathematical Statistics. A Decision Theoretic Approach 1967

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Textbook in PDF format The theory of games is a part of the rich mathematical legacy left by John von Neumann, one of the outstanding mathematicians of our era. Although others — notably Emil Borel — preceded him in formulating a theory of games, it was von Neumann who with the publication in 1927 of a proof of the minimax theorem for finite games laid the foundation for the theory of games as it is known today. Von Neumann's work culminated in a book written in collaboration with Oskar Morgen-stern entitled Theory of Games and Economic Behavior published in 1944. At about the same time, statistical theory was being given an increasingly rigorous mathematical foundation in a series of papers by J. Neyman and Egon Pearson. Statistical theory until that time, as developed by Karl Pearson, R. A. Fisher, and others had lacked the precise mathematical formulation, supplied by Neyman and Pearson, that allows the delicate foundational questions involved to be treated rigorously. Apparently it was Abraham Wald who first appreciated the connections between the theory of games and the statistical theory of Neyman and Pearson, and who recognized the advantages of basing statistical theory-on the theory of games. Wald's theory of statistical decisions, as it is called, generalizes and simplifies the Neyman-Pearson theory by unifying, that is, by treating problems considered as distinct in the Neyman-Pearson theory as special cases of the decision theory problem. Preface Game Theory and Decision Theory The Main Theorems of Decision Theory Distributions and Sufficient Statistics Invariant Statistical Decision Problems Testing Hypotheses Multiple Decision Problems Sequential Decision Problems References Index Solutions to Selected Exercises