Estimation of the sub-Gaussian parameter
Researchers have developed a new method for estimating the sub-Gaussian parameter of a random variable, a measure related to its variance. The proposed estimator is shown to be consistent and achieves convergence rates of $O_p(n^{-1/2})$ under certain conditions, with minimax optimality demonstrated in specific cases. The study also establishes lower bounds for the minimax risk across all sub-Gaussian distributions, interpolating between $\Omega(1/\log n)$ and $\Omega(1)$. The estimator's practical utility is highlighted through its application in Gene Ontology enrichment studies for constructing p-values in permutation tests. AI
IMPACT Introduces a new statistical tool that could enhance data analysis in various fields, including those that might utilize AI.