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.
@article{1176344009,
author = {Basar, Tamer},
title = {Optimum Fisherian Information for Multivariate Distributions},
journal = {Ann. Statist.},
volume = {5},
number = {1},
year = {1977},
pages = { 1240-1244},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344009}
}
Basar, Tamer. Optimum Fisherian Information for Multivariate Distributions. Ann. Statist., Tome 5 (1977) no. 1, pp. 1240-1244. http://gdmltest.u-ga.fr/item/1176344009/