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New estimator for sub-Gaussian parameter achieves root-n rate

By PulseAugur Editorial · [2 sources] ·

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.

RANK_REASON This is a research paper published on arXiv detailing a new statistical estimation method. [lever_c_demoted from research: ic=2 ai=0.4]

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Jason Liu, Min Xu, Jinchuan Xing ·

    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…

  2. arXiv stat.ML TIER_1 English(EN) · Jinchuan Xing ·

    Estimation of the sub-Gaussian parameter

    The sub-Gaussian parameter (also called the variance proxy) of a mean-zero random variable $X$ is defined as $ξ^2_* = \sup_{λ\in \mathbb{R}} L(λ)$ where $L(λ) = \frac{2}{λ^2} \log \mathbb{E} e^{λX}$ is a weighted cumulant generating function. Despite the ubiquity of sub-Gaussian …

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