# Extremal Families And Systems Of Sufficient Statistics (lecture Notes In Statistics)

by Steffen L. Lauritzen /
1988 / English / PDF

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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.

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.