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Statistics - Statistical Theory and Methods | Mathematical Statistics - Essays on History and Methodology

Mathematical Statistics

Essays on History and Methodology

Pfanzagl, Johann

2016, Approx. 320 p.

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ISBN 978-3-642-31084-3

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  • ​The book presents a detailed description of the development of statistical theory around 1950
  • An important aspect is the interplay between the increasing role of refined mathematical techniques and the corresponding development of methodological concepts
  • It tries to discuss missed opportunities Points out errors in the proofs of important theorems, Clears up questions of priorities

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.

Content Level » Upper undergraduate

Keywords » Convolution Theorem - Descriptive Statistics - Estimation - Methodology - Statistical Theory

Related subjects » History of Mathematical Sciences - Probability Theory and Stochastic Processes - Statistical Theory and Methods

Table of contents 

​Essay 1: Sufficiency.- Essay 2: Descriptive Statistics.- Essay 3: Optimality of unbiased estimators: nonasymptotic theory.- Essay 4: Asymptotic optimality of estimators.

Distribution rights 

Distribution rights for India: Researchco Book Centre, New Delhi, India

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