This book presents a detailed description of the development of
statistical theory. In the mid twentieth century, the development of
mathematical statistics underwent an enduring change, due to the advent
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, because a meaningful
concept of optimality (based on the 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, this book presents a detailed
description of how the use of mathematical methods stimulated the
development of a statistical theory. Primarily focused on methodology,
questionable proofs and neglected questions of priority, the book offers
an intriguing resource for researchers in theoretical statistics, and
can also serve as a textbook for advanced courses in statisticc.