Chunk #49 — Materials and Methods — Derivation of the sum-score

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Fast and Rigorous Computation of Gene and Pathway Scores from SNP-Based Summary Statistics.

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The eigenvalue decomposition of Σ is Σ=ΓΛΓT, where Γ and Λ are the matrices of eigenvectors and eigenvalues, respectively. We see that multiplying z with the inverse of the square-root of Σ leads to a vector of independent random variables. Let y be defined as y=Λ−1/2ΓTz, then y∼Nn(0,In).