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Numerical evaluation of methods approximating the distribution of a large quadratic form in normal variables

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  • Chen, Tong
  • Lumley, Thomas

Abstract

Quadratic forms of Gaussian variables occur in a wide range of applications in statistics. They can be expressed as a linear combination of chi-squareds. The coefficients in the linear combination are the eigenvalues λ1,…,λn of ΣA, where A is the matrix representing the quadratic form and Σ is the covariance matrix of the Gaussians. The previous literature mostly deals with approximations for small quadratic forms (n<10) and moderate p-values (p>10−2). Motivated by genetic applications, moderate to large quadratic forms (300

Suggested Citation

  • Chen, Tong & Lumley, Thomas, 2019. "Numerical evaluation of methods approximating the distribution of a large quadratic form in normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 75-81.
    • Handle: RePEc:eee:csdana:v:139:y:2019:i:c:p:75-81
    DOI: 10.1016/j.csda.2019.05.002
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    References listed on IDEAS

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    1. Duchesne, Pierre & Lafaye De Micheaux, Pierre, 2010. "Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 858-862, April.
    2. R. W. Farebrother, 1984. "The Distribution of a Positive Linear Combination of X2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(3), pages 332-339, November.
    3. Robert B. Davies, 1980. "The Distribution of a Linear Combination of χ2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 323-333, November.
    4. Liu, Huan & Tang, Yongqiang & Zhang, Hao Helen, 2009. "A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 853-856, February.
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