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Introduction

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Mathematical Statistics

Part of the book series: Springer Series in Statistics ((PSS))

Abstract

The introductory Chapter 1 emphasizes the point of view taken in the four essays of the book: Assertions and assumptions on statistical procedures should be of operational significance. A number of statistical concepts are discussed from this standpoint. The increasing role of mathematics in the development of meaningful results is emphasized. Reliance on statistical “principles” without operational meaning is criticized, as is the tendency to develop overly general “universal theories”.

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Notes

  1. 1.

    Curiously, the very first sentence in Neyman’s paper is: “The theory of confidence intervals was started by the author in 1930.” However, forerunners are Laplace (1812) and Poisson (1837). If there had been any doubts about the interpretation of “covering probability”, they were settled by Wilson (1927).

  2. 2.

    Having been undecided between probability and statistics, Halmos made up his mind as early as 1937: “I’ll take probability, and to hell with Fisher” (see Halmos 1985, p. 65). See, however, his fundamental contribution to the concept of “sufficiency” in Halmos and Savage (1949).

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  1. Mathematical Institute, University of Cologne, Cologne, Germany

    Johann Pfanzagl

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  1. Johann Pfanzagl
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Pfanzagl, J. (2017). Introduction. In: Mathematical Statistics. Springer Series in Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31084-3_1

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