A simple proof for the multivariate Chebyshev inequality
Statistics Theory
2013-05-27 v1 Statistics Theory
Abstract
In this paper a simple proof of the Chebyshev's inequality for random vectors obtained by Chen (arXiv:0707.0805v2, 2011) is obtained. This inequality gives a lower bound for the percentage of the population of an arbitrary random vector X with finite mean E(X) and a positive definite covariance matrix V=Cov(X) whose Mahalanobis distance with respect to V to the mean E(X) is less than a fixed value. The proof is based on the calculation of the principal components.
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Cite
@article{arxiv.1305.5646,
title = {A simple proof for the multivariate Chebyshev inequality},
author = {Jorge Navarro},
journal= {arXiv preprint arXiv:1305.5646},
year = {2013}
}
Comments
4 pages