In the middle of the last century the development of mathematical statistics underwent an enduring change, due to the use of more refined mathematical tools.
New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance. Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, as a meaningful concept of optimality (based on regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson’s Theorem) was not yet available.
The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions.
In four engaging essays, Pfanzagl’s book presents a detailed description of how the use of mathematical methods stimulated the development of a statistical theory.
A book on the history of mathematical statistics would offer a description of who did what and when. Pfanzagl’s book, centred on questions of methodology, points to missed opportunities, questionable proofs, neglected questions of priority, and to the presence of such deficiencies even in recent textbooks.
This detailed description of the fundamental developments in statistical theory around 1950 points out the centrally important interplay between increasingly refined mathematical techniques and the concomitant developments in methodological concepts.
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