On the determinant of the second derivative of a Laplace transform

• 成果类型: Article
• 署名作者: Kokonendji, CC; Seshadri, V
• 署名单位: McGill University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 1813-1827
• 关键词: natural exponential-families; variance functions

摘要

If Ct is a positive measure on R(n) with Laplace transform L(mu), we show that there exists a positive measure v on R(n) such that det L(mu)(n) = L(v). We deduce various corollaries from this result and, in particular, we obtain the Rao-Blackwell estimator of the determinant of the variance of a natural exponential family on R(n) based on (n + 1) observations. A new proof and extensions of Lindsay's results on the determinants of moment matrices are also given. Finally we give a characterization of the Gaussian law in R(n).