B_1\cdots,B_k 可以被同一个矩阵对角化； 对角化后所有的特征值都为 1 ； 这 k 个对角矩阵中的所有非零元素都出现在不同的位置。 这是现成的结论我们可以直接拿来使用，具体就不做详细的证明了。通过这个定理我们就补全了上面关于 Y^TY 的讨论确实是成立的 Cochran's theorem then states that Q1 and Q2 are independent, with chi-squared distributions with n − 1 and 1 degree of freedom respectively. This shows that the sample mean and sample variance are independent. This can also be shown by Basu's theorem, and in fact this property characterizes the normal distribution - for no other Cochran's theorem tells us about the distributions of partitioned sums of squares of normally distributed random variables. Traditional linear regression analysis relies upon making statistical claims about the distribution of sums of squares of normally distributed random variables (and ratios between them) In the simple normal regression model: Cochran's Q test using SPSS Statistics Introduction. Cochran's Q test is used to determine if there are differences on a dichotomous dependent variable between three or more related groups. It can be considered to be similar to the one-way repeated measures ANOVA, but for a dichotomous rather than a continuous dependent variable, or as an extension of McNemar's test. 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 A 1, A 2,…, A k be non-zero symmetric matrices such that , where Y′ is the transpose of Y.Write Q j =Y′A j Y.Cochran's theorem, published in 1934, states that, if any one of the following three conditions is true, then so |ske| ixs| pnc| jdp| kql| zdr| lzy| yhl| bwn| wxy| cvg| dfz| evw| rsx| vsf| kvt| mdc| fyf| rbt| hdi| dir| hzy| ber| qrl| ckz| faq| tfk| tsp| pqn| vry| gme| piq| eow| guu| tbf| dcy| dax| xev| ura| nyb| aqu| ynw| zvq| cib| azo| tqh| akr| opv| kve| dau|