The distribution of quadratic forms in a normal system, with applications to the analysis of covariance

By W. G. Cochran, J. Wishart. 1934

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The Curse of Recursion: Training on Generated Data Makes Models Forget (2023, background): “In particular, it is well known [Cochran, 1934] that μ1 and σ1 are independent, with μ1 ∼ N (μ, σ 2 M0 ) and (M0 − 1)σ(2) 1 ∼ σ2Γ(M0−1 2 , 1 2 ).”
Foundations of Linear and Generalized Linear Models (2015, background): “The following key result also follows from Cochran (1934), building on the first result.”
Extending the Akaike Information Criterion to Mixture Regression Models (2007, unknown): “Next, applying results of Cochran (1934), we find that ε′k(W 0 k) 1/2H0k(W 0 k) 1/2εk/(σ 0 k ) 2 and ε′k(W 0 k) 1/2(I− H0k)(W 0 k) 1/2εk/(σ 0 k ) 2 are independent chi-squared distributions with the degrees of freedom tr(H0kW 0 k) = νk1 = p0 and tr{(I − H0k)W 0 k} = δk1 = δk2 = n0k − p0, where εk…”