Optimum Fisherian Information for Multivariate Distributions
The Annals of Statistics · 1977 · Volume 5 · Issue 6
Abstract
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.
Keywords
62B10, 62E10, 62F10, 62H05, Fisherian information, Gaussian distribution, Multivariate distributions, robust estimation
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