Approximations in Statistics from a Decision-Theoretical Viewpoint

José M. Bernardo
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José M. Bernardo: Universidad de Valencia, Departamento de Estadística

A chapter in Probability and Bayesian Statistics, 1987, pp 53-60 from Springer

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.

Keywords: Utility Function; Decision Problem; Random Vector; True Distribution; Logarithmic Divergence (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-1885-9_6

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DOI: 10.1007/978-1-4613-1885-9_6

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