Can the bounds in the multivariate Chebyshev inequality be attained?

Jorge Navarro

Statistics & Probability Letters, 2014, vol. 91, issue C, 1-5

Abstract: Chebyshev’s inequality was recently extended to the multivariate case. In this paper we prove that the bounds in the multivariate Chebyshev’s inequality for random vectors can be attained in the limit. Hence, these bounds are the best possible bounds for this kind of regions.

Keywords: Chebyshev (Tchebysheff) inequality; Mahalanobis distance; Principal components; Ellipsoid (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2014.03.028

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