标题： 高斯二次型的改进浓度界限 显示英文标题

标题： Improved Concentration Bounds for Gaussian Quadratic Forms

摘要： 对于一大类单调函数$f$，我们为二次型$Q_f \sim \sum\limits_{i=1}^n f(\eta_i) (Z_i + \delta_i)^2$开发了一个类似 Chernoff 的集中不等式，其中$Z_i \sim N(0,1)$。 该不等式以迹的形式表示，这些迹的计算速度快，使其在高维筛选应用中用于界定 p 值非常有用。 我们得到的界限比之前开发的界限要紧得多，我们通过数值例子来说明这一点。 显示英文摘要

摘要： For a wide class of monotonic functions $f$, we develop a Chernoff-style concentration inequality for quadratic forms $Q_f \sim \sum\limits_{i=1}^n f(\eta_i) (Z_i + \delta_i)^2$, where $Z_i \sim N(0,1)$. The inequality is expressed in terms of traces that are rapid to compute, making it useful for bounding p-values in high-dimensional screening applications. The bounds we obtain are significantly tighter than those that have been previously developed, which we illustrate with numerical examples.