An extension of the multivariate Chebyshev's inequality to a random vector with a singular covariance matrix

DOI10.1080/03610926.2014.941499zbMath1385.60039OpenAlexW2349467063MaRDI QIDQ2817149

Katarzyna Budny

Publication date: 29 August 2016

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610926.2014.941499

zbMATH Keywords

random vectormultivariate normal distributionChebyshev inequalitysingular covariance matrix

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Probability distributions: general theory (60E05)

Related Items (4)

The echelon Markov and Chebyshev inequalities ⋮ The multivariate Markov and multiple Chebyshev inequalities ⋮ The variance of the power of a shifted random variable with applications ⋮ Improved probability inequalities for Mardia's coefficient of kurtosis

Cites Work

• Unnamed Item
• Chebyshev's inequality for Banach-space-valued random elements
• Chebyshev's inequality for Hilbert-space-valued random elements
• A generalization of Chebyshev's inequality for Hilbert-space-valued random elements
• Can the bounds in the multivariate Chebyshev inequality be attained?
• A Multivariate Tchebycheff Inequality
• Multivariate Chebyshev Inequalities
• A very simple proof of the multivariate Chebyshev's inequality
• INEQUALITIES FOR MULTIVARIATE FREQUENCY DISTRIBUTIONS

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