Thomas Lumley • 9/13/2024

Two approaches to approximating sums of chisquareds

This technical article analyzes methods for approximating the distribution of quadratic forms in Gaussian variables, which are sums of weighted chi-squared variables. It focuses on genomic applications with large sample sizes and small tail probabilities, comparing the Satterthwaite approximation (matching two moments), the Liu approximation (matching three cumulants), and leading-term approximations. It evaluates their relative errors in estimating higher cumulants and tail probabilities, highlighting the limitations of each method in extreme tails.

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#statistics #Computational Methods #Quadratic Forms