Strengthened Chernoff-type variance bounds

DOI10.3150/12-BEJ484zbMath1294.60027arXiv1107.1754MaRDI QIDQ2444666

Giorgos Afendras, Nickos Papadatos

Publication date: 10 April 2014

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.1754

zbMATH Keywords

derivativesintegrated Pearson familyChernoff-type variance boundsRodrigues polynomials

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15)

Related Items (7)

On the property of multivariate generalized hyperbolic distribution and the Stein-type inequality ⋮ On infinite covariance expansions ⋮ How a probabilistic analogue of the mean value theorem yields stein-type covariance identities ⋮ Unified extension of variance bounds for integrated Pearson family ⋮ Maximal correlation in a non-diagonal case ⋮ Orthogonal polynomials in the cumulative Ord family and its application to variance bounds ⋮ Some Stein-type inequalities for multivariate elliptical distributions and applications

Cites Work

• An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds
• Matrix variance inequalities for multivariate distributions
• Covariance matrix inequalities for functions of beta random variables
• On upper bounds for the variance of functions of random variables
• On an inequality of Chernoff
• Variance bounds using a theorem of Polya
• Variance bounds by a generalization of the Cauchy-Schwarz inequality
• Characterizations of distributions by variance bounds
• Density questions in the classical theory of moments
• A note on an inequality involving the normal distribution
• An inequality for the multivariate normal distribution
• On upper and lower bounds for the variance of a function of a random variable
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• Variance inequalities for functions of Gaussian variables
• Closed form summation for classical distributions: variations on a theme of de Moivre
• A matrix variance inequality
• On matrix variance inequalities
• Continuity of Solutions of Parabolic and Elliptic Equations
• Integrated Pearson family and orthogonality of the Rodrigues polynomials: A review including new results and an alternative classification of the Pearson system
• Systems of Polynomials Connected with the Charlier Expansions and the Pearson Differential and Difference Equations
• On a Certain Class of Orthogonal Polynomials
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