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Approximations in Statistics from a Decision-Theoretical Viewpoint

In: Probability and Bayesian Statistics

Author

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  • José M. Bernardo

    (Universidad de Valencia, Departamento de Estadística)

Abstract

Summary The approximation of the probability density p(.) of a random vector x∊X by another (possibly more convenient) probability density q(.) which belongs to a certain class Q is analyzed as a decision problem where the action space is the class Qof available approximations, the relevant uncertain event is the actual value of the vector x and the utility function is a proper scoring rule. The logarithmic divergence is shown to play a rather special role within this approach. The argument lies entirely within a Bayesian framework.

Suggested Citation

  • José M. Bernardo, 1987. "Approximations in Statistics from a Decision-Theoretical Viewpoint," Springer Books, in: R. Viertl (ed.), Probability and Bayesian Statistics, pages 53-60, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-1885-9_6
    DOI: 10.1007/978-1-4613-1885-9_6
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