An efficient and accurate approximation to the distribution of quadratic forms of Gaussian variables

05/02/2020

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by   Hong Zhang, et al.

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Fast and accurate calculation for the distributions of Quadratic forms of centered Gaussian variables is of interest in computational statistics. This paper presents a novel numerical procedure to efficiently compute the moments of a given quadratic form. Based on that, a gamma distribution with matched skewness-kurtosis ratio is proposed to approximate its distribution. Comparing with existing methods, the new method is significantly more accurate in getting the right-tail probability. The new method may facilitate the hypothesis testing in the analysis of big data, where efficient and accurate calculation of small p-values is desired. Relevant R functions are provided in the Supplementary Materials.