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Multivariate Chebyshev inequality with estimated mean and variance

Abstract:
A variant of the well-known Chebyshev inequality for scalar random variables can be formulated in the case where the mean and variance are estimated from samples. In this paper we present a generalization of this result to multiple dimensions where the only requirement is that the samples are independent and identically distributed. Furthermore, we show that as the number of samples tends to infinity our inequality converges to the theoretical multidimensional Chebyshev bound.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1080/00031305.2016.1186559

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Engineering Science
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Engineering Science
Van Parys, BPG More by this author
Publisher:
Taylor and Francis Publisher's website
Journal:
American Statistician Journal website
Volume:
71
Issue:
2
Pages:
123-127
Publication date:
2016-05-05
Acceptance date:
2016-04-27
DOI:
EISSN:
1537-2731
ISSN:
0003-1305
URN:
uuid:e71796b6-3d03-4789-b38d-8cff846aca09
Source identifiers:
620171
Local pid:
pubs:620171

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