Lower variance bounds and a new proof of the central limit theorem

DOI10.1016/0047-259X(92)90032-BzbMath0770.60021MaRDI QIDQ1206446

Theophilos Cacoullos, V. Papathanasiou

Publication date: 1 April 1993

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

inequalitiesmultivariate central limit theoremlower variance bounds

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items (10)

Covariance kernel and the central limit theorem in the total variation distance ⋮ On upper bounds for the variance of functions of random variables with weighted distributions ⋮ Characterizations of distributions by generalizations of variance bounds and simple proofs of the CLT ⋮ First-order covariance inequalities via Stein's method ⋮ Converse Poincaré-type inequalities for convex functions ⋮ A matrix variance inequality ⋮ Further results based on Chernoff-type inequalities ⋮ Variational inequalities for arbitrary multivariate distributions ⋮ Some results on lower variance bounds useful in reliability modeling and estimation ⋮ Relaxing the Gaussian assumption in shrinkage and SURE in high dimension

Cites Work

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• A differential version of the Efron-Stein inequality: Bounding the variance of a function of an infinitely divisible variable
• Characterizations of distributions by variance bounds
• 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 an Inequality and a Related Characterization of the Normal Distribution
• Poincaré-type inequalities via stochastic integrals
• Another Characterization of the Normal Law and a Proof of the Central Limit Theorem Connected with it

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