Review: Kenneth S. Miller, Multidimensional Gaussian Distributions

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On multidimensional generalized Cramér-Rao inequalities, uncertainty relations and characterizations of generalized q-Gaussian distributions

In the present work, we show how the generalized Cramér-Rao inequality for the estimation of a parameter, presented in a recent paper, can be extended to the mutidimensional case with general norms on Rn, and to a wider context. As a particular case, we obtain a new multidimensional Cramér-Rao inequality which is saturated by generalized q-Gaussian distributions. We also give another related Cr...

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ژورنال

عنوان ژورنال: The Annals of Mathematical Statistics

سال: 1966

ISSN: 0003-4851

DOI: 10.1214/aoms/1177699627