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Some Characteristic Properties of the Fisher Information Matrix via Cacoullos-Type Inequalities

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  • Papathanasiou, V.

Abstract

Some lower bounds for the variance of a function g of a random vector X are extended to a wider class of distributions. Using these bounds, some useful inequalities for the Fisher information are obtained for convolutions and linear combinations of random variables. Finally, using these inequalities, simple proofs are given of classical characterizations of the normal distribution, under certain restrictions, including the matrix analogue of the Darmois-Skitovich result.

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  • Papathanasiou, V., 1993. "Some Characteristic Properties of the Fisher Information Matrix via Cacoullos-Type Inequalities," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 256-265, February.
    • Handle: RePEc:eee:jmvana:v:44:y:1993:i:2:p:256-265
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    Cited by:

    1. Takis Papaioannou & Kosmas Ferentinos & Charalampos Tsairidis, 2007. "Some Information Theoretic Ideas Useful in Statistical Inference," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 307-323, June.
    2. Gibilisco, Paolo & Imparato, Daniele & Isola, Tommaso, 2008. "Stam inequality on," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1851-1856, September.
    3. Papadatos, N. & Papathanasiou, V., 1998. "Variational Inequalities for Arbitrary Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 154-168, November.

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