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) |
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Pages (from-to) | 123-127 |
Number of pages | 5 |
Journal | American Statistician |
Volume | 71 |
Issue number | 2 |
DOIs | |
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