A theorem, given by Cochran in 1934, concerning sums of chi-squared variables. Let Y represent an n×1 vector of independent standard normal random variables and let A1, A2,…, Ak be non-zero symmetric matrices such that , where Y′ is the transpose of Y. Write Qj=Y′AjY. Cochran's theorem, published in 1934, states that, if any one of the following three conditions is true, then so are the other two:
Subjects: Probability and Statistics.