Multivariate Chebyshev Inequality With Estimated Mean and Variance

Bartolomeo Stellato; Bart P.G. Van Parys; Paul J. Goulart

doi:10.1080/00031305.2016.1186559

Multivariate Chebyshev Inequality With Estimated Mean and Variance

Bartolomeo Stellato, Bart P.G. Van Parys, Paul J. Goulart

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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 article, 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 multi-dimensional Chebyshev bound.

Original language	English (US)
Pages (from-to)	123-127
Number of pages	5
Journal	American Statistician
Volume	71
Issue number	2
DOIs	https://doi.org/10.1080/00031305.2016.1186559
State	Published - Apr 3 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

Keywords

Chebyshev’s inequality
Probability bounds
Sampling

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10.1080/00031305.2016.1186559

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KW - Sampling

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Multivariate Chebyshev Inequality With Estimated Mean and Variance

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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