Open Access
August 1996 On the determinant of the second derivative of a Laplace transform
Célestin C. Kokonendji, V. Seshadri
Ann. Statist. 24(4): 1813-1827 (August 1996). DOI: 10.1214/aos/1032298297

Abstract

If $\mu$ is a positive measure on $\mathbb{R}^n$ with Laplace transform $L_{\mu}$ , we show that there exists a positive measure $\mu$ on $\mathbb{R}^n$ such that det $L_{\mu}^'' = L_{\nu}$. 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 $\mathbb{R}^n$ 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 $\mathbb{R}^n$.

Citation

Download Citation

Célestin C. Kokonendji. V. Seshadri. "On the determinant of the second derivative of a Laplace transform." Ann. Statist. 24 (4) 1813 - 1827, August 1996. https://doi.org/10.1214/aos/1032298297

Information

Published: August 1996
First available in Project Euclid: 17 September 2002

zbMATH: 0868.62047
MathSciNet: MR1416662
Digital Object Identifier: 10.1214/aos/1032298297

Subjects:
Primary: 60E10 , 62E10

Keywords: characterization , determinant , generalized variance , Laplace transform , Natural exponential family , quadratic variance functions

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 4 • August 1996
Back to Top