Generalized variance and exponential families

• 成果类型: Article
• 署名作者: Hassairi, A
• 署名单位: Universite de Sfax; Faculty of Sciences Sfax
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1018031116
• 发表日期: 1999
• 页码: 374-385
• 关键词: conjugate priors; transform; r(d)

摘要

Let mu be a positive measure on R-d and let F(mu) = {P(theta, mu); theta is an element of Theta} be the natural exponential family generated by mu. The aim of this paper is to show that if mu is infinitely divisible then the generalized variance of mu, i.e., the determinant of the covariance operator of P(theta, mu), is the Laplace transform of some positive measure rho(mu) on R-d. We then investigate the effect of the transformation mu --> rho(mu) and its implications for the skewness vector and the conjugate prior distribution families of F(mu).