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Comparison of Finite Experiments

  • H. Heyer
Part of the Springer Series in Statistics book series (SSS)

Abstract

In Section 19 we dealt with general decision problems of the form \( \bar{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{D}}} = (I,D,V) \)= (I,D,V), where I: = (ΩI,AI) and D: = (ΩD,AD) denoted measurable spaces and V a set of separately measurable functions on ΩI × ΩD. From now on, and for the remainder of the chapter, we shall specialize the general framework in two steps: First we shall restrict our attention to decision problems of the form <Inline>2</Inline>k(I): = (I,Dk,V) with Dk: = {1,…,k} (k ≥1) as the decision space and the set V of all bounded, separately measurable functions on ΩI × ΩD as the set of loss functions. Later we shall consider decision problems of the form \( {\bar{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{D}}}_k}\,(I): = (I,{D_k},V) \)k (In) with In = {l, …, n} (n ≥ 1).

Keywords

Decision Problem Convex Subset Standard Measure Standard Experiment Standard Simplex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • H. Heyer
    • 1
  1. 1.Mathematisches InstitutUniversität TübingenTübingen 1West Germany

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