期刊
AMERICAN STATISTICIAN
卷 71, 期 2, 页码 123-127出版社
AMER STATISTICAL ASSOC
DOI: 10.1080/00031305.2016.1186559
关键词
Chebyshev's inequality; Probability bounds; Sampling
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.
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