Strengthened Chernoff-type variance bounds

Abstract

Let $X$ be an absolutely continuous random variable from the integrated Pearson family and assume that $X$ has finite moments of any order. Using some properties of the associated orthonormal polynomial system, we provide a class of strengthened Chernoff-type variance bounds.

Published in at http://dx.doi.org/10.3150/12-BEJ484 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (3)

• An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds
• On matrix variance inequalities
• Integrated Pearson family and orthogonality of the Rodrigues polynomials: A review including new results and an alternative classification of the Pearson system

Cited by in corpus (5)

• Orthogonal polynomials in the Cumulative Ord family and its application to variance bounds
• On infinite covariance expansions
• Unified extension of variance bounds for integrated Pearson family
• A note on a variance bound for the multinomial and the negative multinomial distribution
• Gauss and the identity function -- a tale of characterizations of the normal distribution