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Extremal Families and Systems of Sufficient Statistics

  • Steffen L. Lauritzen

Part of the Lecture Notes in Statistics book series (LNS, volume 49)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Back Matter
    Pages 260-268

About this book

Introduction

The pOint of view behind the present work is that the connection between a statistical model and a statistical analysis-is a dua­ lity (in a vague sense). In usual textbooks on mathematical statistics it is often so that the statistical model is given in advance and then various in­ ference principles are applied to deduce the statistical ana­ lysis to be performed. It is however possible to reverse the above procedure: given that one wants to perform a certain statistical analysis, how can this be expressed in terms of a statistical model? In that sense we think of the statistical analysis and the stati­ stical model as two ways of expressing the same phenomenon, rather than thinking of the model as representing an idealisation of "truth" and the statistical analysis as a method of revealing that truth to the scientist. It is not the aim of the present work to solve the problem of giving the correct-anq final mathematical description of the quite complicated relation between model and analysis. We have rather restricted ourselves to describe a particular aspect of this, formulate it in mathematical terms, and then tried to make a rigorous and consequent investigation of that mathematical struc­ ture.

Keywords

Likelihood Maxima mathematical statistics statistical model statistics

Authors and affiliations

  • Steffen L. Lauritzen
    • 1
  1. 1.Department of Mathematics and Computer ScienceInstitute of Electronic Systems, Aalborg UniversityAalborgDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1023-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96872-8
  • Online ISBN 978-1-4612-1023-8
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site