Paper

Estimation of the sub-Gaussian parameter

arXiv:2606.06384v1 Announce Type: cross Abstract: The sub-Gaussian parameter (also called the variance proxy) of a mean-zero random variable $X$ is defined as $\xi^2_* = \sup_{\lambda \in \mathbb{R}} L(\lambda)$ where $L(\lambda) = \frac{2}{\lambda^2} \log \mathbb{E} e^{\lambda X}$ is a weighted cumulant generating function. Despite the ubiquity of sub-Gaussian random variables, the estimation of $\xi^2_*$ has received little attention and is not yet well understood. In this work, we study a natural estimator of $\xi^2_*$ based on constrained maximization of the empirical analogue of $L$. We…

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