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RESEARCH PRODUCT

Approximations in Statistics from a Decision-Theoretical Viewpoint

José M. Bernardo

subject

Class (set theory)Multivariate random variableScoring ruleStatisticsProbability density functionFunction (mathematics)Decision problemDivergence (statistics)MathematicsEvent (probability theory)

description

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.

yearjournalcountryeditionlanguage
1987-01-01
https://doi.org/10.1007/978-1-4613-1885-9_6