• DOI:10.1080/00031305.2016.1186559
Corpus ID: 53407286

Multivariate Chebyshev Inequality With Estimated Mean and Variance

@article{Stellato2015MultivariateCI,
  title={Multivariate Chebyshev Inequality With Estimated Mean and Variance},
  author={B. Stellato and Bart P. G. Van Parys and P. Goulart},
  journal={The American Statistician},
  year={2015},
  volume={71},
  pages={123 - 127}
}

• B. Stellato, Bart P. G. Van Parys, P. Goulart
• Published 2015
• Mathematics
• The American Statistician

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.