A very simple proof of the multivariate Chebyshev's inequality
A very simple proof of the multivariate Chebyshev's inequality
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DOI：
10.1080/03610926.2013.873135
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发表时间：
2016-05
期刊：
影响因子：
--
通讯作者：
J. Navarro
中科院分区：
文献类型：
--
作者：
J. Navarro
Abstract In this short note, a very simple proof of the Chebyshev's inequality for random vectors is given. This inequality provides a lower bound for the percentage of the population of an arbitrary random vector X with finite mean μ = E(X) and a positive definite covariance matrix V = Cov(X) whose Mahalanobis distance with respect to V to the mean μ is less than a fixed value. The main advantage of the proof is that it is a simple exercise for a first year probability course. An alternative proof based on principal components is also provided. This proof can be used to study the case of a singular covariance matrix V.
