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A generalization of Chebyshev’s inequality for Hilbert-space-valued random elements

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  • Budny, Katarzyna

Abstract

We obtain a new generalization of Chebyshev’s inequality for random vectors. Then we extend this result to random elements taking values in a separable Hilbert space.

Suggested Citation

  • Budny, Katarzyna, 2014. "A generalization of Chebyshev’s inequality for Hilbert-space-valued random elements," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 62-65.
    • Handle: RePEc:eee:stapro:v:88:y:2014:i:c:p:62-65
    DOI: 10.1016/j.spl.2014.01.021
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    References listed on IDEAS

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    1. Zhou, Ling & Hu, Ze-Chun, 2012. "Chebyshev’s inequality for Banach-space-valued random elements," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 925-931.
    2. Prakasa Rao, B.L.S., 2010. "Chebyshev's inequality for Hilbert-space-valued random elements," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1039-1042, June.
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    Cited by:

    1. Budny Katarzyna, 2019. "Power Generalization Of Chebyshev’S Inequality – Multivariate Case," Statistics in Transition New Series, Statistics Poland, vol. 20(3), pages 155-170, September.
    2. Budny, Katarzyna, 2022. "The variance of the power of a shifted random variable with applications," Statistics & Probability Letters, Elsevier, vol. 182(C).
    3. Budny, Katarzyna, 2022. "Improved probability inequalities for Mardia’s coefficient of kurtosis," Statistics & Probability Letters, Elsevier, vol. 191(C).
    4. Bhat, M. Ashraf & Kosuru, G. Sankara Raju, 2022. "Generalizations of some concentration inequalities," Statistics & Probability Letters, Elsevier, vol. 182(C).
    5. Katarzyna Budny, 2019. "Power Generalization Of Chebyshev’S Inequality – Multivariate Case," Statistics in Transition New Series, Polish Statistical Association, vol. 20(3), pages 155-170, September.
    6. Navarro, Jorge, 2014. "Can the bounds in the multivariate Chebyshev inequality be attained?," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 1-5.

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