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November, 1977 Optimum Fisherian Information for Multivariate Distributions
Tamer Basar
Ann. Statist. 5(6): 1240-1244 (November, 1977). DOI: 10.1214/aos/1176344009


It is shown that within the class of all multivariate distributions depending on a location parameter (and satisfying certain smoothness conditions) and with a weighted norm constraint on the covariance matrix, the one with minimum Fisherian information is the Gaussian distribution. This result is then used in obtaining a tight upper bound on the error of estimating an unknown random vector observed in additive Gaussian noise under quadratic loss.


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Tamer Basar. "Optimum Fisherian Information for Multivariate Distributions." Ann. Statist. 5 (6) 1240 - 1244, November, 1977.


Published: November, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0371.62078
MathSciNet: MR488408
Digital Object Identifier: 10.1214/aos/1176344009

Primary: 62E10
Secondary: 62B10 , 62F10 , 62H05

Keywords: Fisherian information , Gaussian distribution , Multivariate distributions , robust estimation

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 6 • November, 1977
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