%0 Generic %1 stellato2015multivariate %A Stellato, Bartolomeo %A Van Parys, Bart %A Goulart, Paul J. %D 2015 %K proba %T Multivariate Chebyshev Inequality with Estimated Mean and Variance %U http://arxiv.org/abs/1509.08398 %X 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 multi-dimensional Chebyshev bound.

@misc{stellato2015multivariate, 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 multi-dimensional Chebyshev bound.}, added-at = {2016-03-31T06:30:57.000+0200}, author = {Stellato, Bartolomeo and Van Parys, Bart and Goulart, Paul J.}, biburl = {https://www.bibsonomy.org/bibtex/21a68729483ea37a5a3bfbaeb336ddb97/pixor}, description = {1509.08398v2.pdf}, interhash = {2e1e5ae778a9d7b7a82e2a843e092acd}, intrahash = {1a68729483ea37a5a3bfbaeb336ddb97}, keywords = {proba}, note = {cite arxiv:1509.08398v2.pdf}, timestamp = {2016-03-31T06:30:57.000+0200}, title = {Multivariate Chebyshev Inequality with Estimated Mean and Variance}, url = {http://arxiv.org/abs/1509.08398}, year = 2015 }