A New Generalization of Chebyshev Inequality for Random Vectors

TL;DR

This paper introduces a novel generalization of Chebyshev inequality for random vectors, which significantly reduces conservativeness compared to the classical version, enhancing probabilistic bounds in multivariate analysis.

Contribution

The paper presents a new, less conservative generalization of Chebyshev inequality specifically for random vectors, improving probabilistic bounds.

Findings

The new inequality is less conservative than classical Chebyshev.

It provides tighter bounds for the probability of deviations in random vectors.

The generalization broadens the applicability of Chebyshev's inequality in multivariate contexts.

Abstract

In this article, we derive a new generalization of Chebyshev inequality for random vectors. We demonstrate that the new generalization is much less conservative than the classical generalization.