当前位置: X-MOL 学术J. Comput. Graph. Stat. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A Fast and Accurate Approximation to the Distributions of Quadratic Forms of Gaussian Variables
Journal of Computational and Graphical Statistics ( IF 2.4 ) Pub Date : 2022-01-01 , DOI: 10.1080/10618600.2021.2000423
Hong Zhang 1 , Judong Shen 1 , Zheyang Wu 2
Affiliation  

Abstract

In computational and applied statistics, it is of great interest to get fast and accurate calculation for the distributions of the quadratic forms of Gaussian random variables. This article presents a novel approximation strategy that contains two developments. First, we propose a fast numerical procedure in computing the moments of the quadratic forms. Second, we establish a general moment-matching framework for distribution approximation, which covers existing approximation methods for the distributions of the quadratic forms of Gaussian variables. Under this framework, a novel moment-ratio method (MR) is proposed to match the ratio of skewness and kurtosis based on the gamma distribution. Our extensive simulations show that (i) MR is almost as accurate as the exact distribution calculation and is much faster; (ii) comparing with existing approximation methods, MR significantly improves the accuracy of approximating far right tail probabilities. The proposed method has wide applications. For example, it is a better choice than existing methods for facilitating hypothesis testing in big data analysis, where fast and accurate calculation of very small p-values are desired. An R package Qapprox that implements related methods is available on CRAN.



中文翻译:

高斯变量二次型分布的快速准确逼近

摘要

在计算和应用统计中,对高斯随机变量的二次形式的分布进行快速准确的计算具有重要意义。本文提出了一种新颖的近似策略,其中包含两个发展。首先,我们提出了一种计算二次型矩的快速数值程序。其次,我们建立了一个用于分布近似的通用矩匹配框架,该框架涵盖了现有的高斯变量二次形式分布的近似方法。在此框架下,提出了一种新的矩比方法(MR)来匹配基于伽马分布的偏度和峰度比。我们广泛的模拟表明 (i) MR 几乎与精确分布计算一样准确,而且速度更快;(ii) 与现有的逼近方法相比,MR 显着提高了逼近极右尾概率的准确性。所提出的方法具有广泛的应用。例如,它是比现有方法更好的选择,用于促进大数据分析中的假设检验,其中快速准确地计算非常小的需要p值。CRAN 上提供了一个实现相关方法的 R 包Qapprox 。

更新日期:2022-01-01
down
wechat
bug