On matrix variance inequalities

Abstract

Olkin and Shepp (2005, J. Statist. Plann. Inference, vol. 130, pp. 351--358) presented a matrix form of Chernoff's inequality for Normal and Gamma (univariate) distributions. We extend and generalize this result, proving Poincare-type and Bessel-type inequalities, for matrices of arbitrary order and for a large class of distributions.

7 pages, submitted for publication

References in corpus (1)

• An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds

Cited by in corpus (4)

• Strengthened Chernoff-type variance bounds
• On infinite covariance expansions
• A note on a variance bound for the multinomial and the negative multinomial distribution
• Stein-type covariance identities: Klaassen, Papathanasiou and Olkin-Shepp type bounds for arbitrary target distributions