On matrix variance inequalities

Olkin and Shepp [2005, A matrix variance inequality. J. Statist. Plann. Inference 130, 351–358] presented a matrix form of Chernoff's inequality for Normal and Gamma (univariate) distributions. We extend and generalize this result, proving Poincaré-type and Bessel-type inequalities, for matrice...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2011-11, Vol.141 (11), p.3628-3631
Main Authors: Afendras, G., Papadatos, N.
Format: Article
Language:English
Subjects:
Cumulative Ord family
Distribution theory
Exact sciences and technology
General topics
Integrated Pearson family
Linear inference, regression
Mathematics
Matrix inequality
Probability and statistics
Probability theory and stochastic processes
Quadratic polynomial
Sciences and techniques of general use
Statistics
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Summary:Olkin and Shepp [2005, A matrix variance inequality. J. Statist. Plann. Inference 130, 351–358] presented a matrix form of Chernoff's inequality for Normal and Gamma (univariate) distributions. We extend and generalize this result, proving Poincaré-type and Bessel-type inequalities, for matrices of arbitrary order and for a large class of distributions.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2011.05.016