We prove that the Esseen's constant $0.4097...$ is valid in the iid Berry--Esseen inequality as long as the sample sizes $n\ge N$. The threshold $N$ is universal over all real summand distributions with positive variance and a finite third absolute moment. In particular, one may take $N=2\left\lceil\exp(10^{17})\right\...
Consider testing a finite composite null $\cP={P_1,\ldots,P_L}$ against a simple alternative $Q$ using $n$ i.i.d. observations. Let $\ell_n$ denote the supremum of the expected log e-value over e-variables that are exact under every $P_i$ and pivotal across the nulls. Zhang, Ramdas, and Wang (2024) showed that $\ell_n$...
Let $X_1,\ldots,X_n$ be independent Gaussian tensors in $\mathbb{R}^{d_1}\otimes\cdots\otimes\mathbb{R}^{d_k}$ with a common covariance matrix given by the Kronecker product of $k$ unknown positive-definite factors, and let $D=\prod_{a=1}^k d_a$ and $d_{\max}=\max_a d_a$. Franks et al. (2026) established condition-numb...
Exhaustive moment fitting in this constant-dimensional space produces a proper mixture and, together with the dimension-free moment characterization of Gaussian mixtures, achieves the optimal Hellinger rate in polynomial arithmetic time for every fixed $k$.
Heng-Zhi He, Guang Cheng· 0 citations
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