A predictivistic interpretation of the multivariatet distribution

SummaryDe Finetti type theorems characterize models in terms of invariance. The idea is to take observables, postulate symmetry and then represent the model as a mixture of standard parametric models. If additional conditions are specified, then the mixing measure can be determined. Invariance under the action of special groups of orthogonal transformations may give results on mixtures of parametric normal distributions (Diaconis, Eaton and Lauritzen, 1992). The additional conditions required to determine the mixing measure in this case can be obtained using results in Diaconis and Ylvisaker (1979, 1985). From these results, we obtain a predictivistic characterization of the multivariatet distribution. Furthermore, we state conditions under which then-dimensional law of sequences of random variables is a location mixture of multivariatet distributions. The results are extended to the case of sequences of orthogonally invariant random vectors.

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