An improvement of Tusnády's inequality in the bulk

A refined determinantal inequality for correlation matrices

Olkin [3] obtained a neat upper bound for the determinant of a correlation matrix. In this note, we present an extension and improvement of his result.

马尔可夫、切比雪夫和切尔诺夫不等式的随机化与可交换改进

Randomized and Exchangeable Improvements of Markov's, Chebyshev's and Chernoff's Inequalities

本文提出马尔可夫、切比雪夫和切尔诺夫不等式的随机化与可交换改进，证明简短且更强，并应用于提升通用推断功效和构建更紧的置信区间。

New-Type Hoeffding's Inequalities and Application in Tail Bounds

It is well known that Hoeffding's inequality has a lot of applications in the signal and information processing fields. How to improve Hoeffding's inequality and find the refinements of its applications have always attracted much attentions. An improvement of Hoeffding inequality was recently given by Hertz \cite{r1}. Eventhough such an improvement is not so big, it still can be used to update many known results with original Hoeffding's inequality, especially for Hoeffding-Azuma inequality for martingales. However, the results in original Hoeffding's inequality and its refinement one by Hertz…

Improvements on removing non-optimal support points in D-optimum design algorithms

We improve the inequality used in Pronzato [2003. Removing non-optimal support points in D-optimum design algorithms. Statist. Probab. Lett. 63, 223-228] to remove points from the design space during the search for a $D$-optimum design. Let $ξ$ be any design on a compact space $\mathcal{X} \subset \mathbb{R}^m$ with a nonsingular information matrix, and let $m+ε$ be the maximum of the variance function $d(ξ,\mathbf{x})$ over all $\mathbf{x} \in \mathcal{X}$. We prove that any support point $\mathbf{x}_{*}$ of a $D$-optimum design on $\mathcal{X}$ must satisfy the inequality $d(ξ,\mathbf{x}_{*}…