“Cochran's theorem”的概念、定义、翻译、参考文献-科学参考

Cochran's theorem

Statistics

A theorem, given by Cochran in 1934, concerning sums of chi-squared variables. Let Y be an n×1 vector of independent standard normal variables (see normal distribution) and let A₁, A₂,…, A_k be non-zero symmetric matrices such that $Cochran's theorem$ where Y′ is the transpose of Y. Write Q_j=Y′A_jY. Cochran's theorem, published in 1934, states that, if any one of the following three conditions is true, then so are the other two:
1. (i) The ranks of A₁, A₂,…, A_k sum to n.
2. (ii) Each of Q₁, Q₂,…, Q_k has a chi-squared distribution.
3. (iii) Each of Q₁, Q₂,…, Q_k is independent of all the others.

单词	Cochran's theorem
释义	Cochran's theorem Statistics A theorem, given by Cochran in 1934, concerning sums of chi-squared variables. Let Y be an n×1 vector of independent standard normal variables (see normal distribution) and let A₁, A₂,…, A_k be non-zero symmetric matrices such that $Cochran's theorem$ where Y′ is the transpose of Y. Write Q_j=Y′A_jY. Cochran's theorem, published in 1934, states that, if any one of the following three conditions is true, then so are the other two: (i) The ranks of A₁, A₂,…, A_k sum to n. (ii) Each of Q₁, Q₂,…, Q_k has a chi-squared distribution. (iii) Each of Q₁, Q₂,…, Q_k is independent of all the others.
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