Zellner (1975), Chaloner and Brant (1988), and Chaloner (1991) used the posterior distributions of the realized errors to define outliers in a linear model. The same concept is used here to define outliers in a state-space model. An effective approach to compute the posterior probabilities of...

In this paper we present a widely applicable definition of the predictive likelihood based on estimators that are either sufficient or approximately sufficient. Under regularity conditions, this predictive likelihood is shown to equal the Bayes prediction density up to terms of order O p(n-1)....

A very general measure of skewness based on the quantiles is introduced, which includes several well-known measures as special cases. Sample versions of our measure may be used as test statistics for testing the hypothesis of symmetry about an unknown value. We provide large sample theory for...