# Extremal Families and Systems of Sufficient Statistics

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

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

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.

Likelihood Maxima mathematical statistics statistical model statistics

- 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

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