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- W2110122189 abstract "1. General remarks. The theorem that has come to be known as Cochran's theorem in works on mathematical statistics was published in these Proceedings in 1934(1). If x 1 , …, x n are independently distributed standard normal deviates, and q 1 , …, q k are k real quadratic forms in the x i with ranks n 1 , …, n k respectively, and such that then Cochran's Theorem II states that a necessary and sufficient condition that q 1 …, q k are independently distributed in χ 2 forms with n 1 , …, n k degrees of freedom is that Σ n j = n. The necessity of the condition is obvious. Cochxan proves its sufficiency by expressing each q j as a sum, involving n j squares of real linear forms in the x i ; it follows easily that the coefficients c i are in fact + 1, and that the transformation is orthogonal. The theorem then follows immediately from the properties of orthogonal transformations in relation to independent normal deviates." @default.
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- W2110122189 date "1952-07-01" @default.
- W2110122189 modified "2023-09-25" @default.
- W2110122189 title "Notes on a theorem of Cochran" @default.
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- W2110122189 doi "https://doi.org/10.1017/s0305004100027845" @default.
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