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- W4383859665 abstract "Let $X$ be a centered random vector in a finite dimensional real inner product space $mathcal{E}$. For a subset $C$ of the ambient vector space $V$ of $mathcal{E}$ and $x,,yin V$, write $xpreceq_C y$ if $y-xin C$. When $C$ is a closed convex cone in $mathcal{E}$, then $preceq_C$ is a pre-order on $V$, whereas if $C$ is a proper cone in $mathcal{E}$, then $preceq_C$ is actually a partial order on $V$. In this paper we give sharp Cantelli's type inequalities for generalized tail probabilities like $text{Pr}{Xsucceq_C b}$ for $bin V$. These inequalities are obtained by ``scalarizing'' $Xsucceq_C b$ via cone duality and then by minimizing the classical univariate Cantelli's bound over the scalarized inequalities." @default.
- W4383859665 created "2023-07-11" @default.
- W4383859665 creator A5068548647 @default.
- W4383859665 date "2023-07-07" @default.
- W4383859665 modified "2023-09-27" @default.
- W4383859665 title "Cantelli's bounds for generalized tail inequalities in Euclidean spaces" @default.
- W4383859665 doi "https://doi.org/10.48550/arxiv.2307.03607" @default.
- W4383859665 hasPublicationYear "2023" @default.
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