設總體的二階矩陣存在,x1,...,xn為其樣本,求xi-(x的拔)與xj-(x的拔...
- 2022-10-21
cov(xi-x拔,xj-x拔)=cov(xi,xj-x拔)+cov(-x拔,xj-x拔)=cov(xi,xj)+cov(xi,-x拔)+cov(-x拔,xj)+cov(-x拔,-x拔)=cov(xi,xj)+cov(x拔,x拔)-2cov(xi,x拔)
=-cov(x1,x拔)-cov(xn,x拔)+cov(x拔,x拔)
cov(xi-x拔,xj-x拔)=cov(xi,xj-x拔)+cov(-x拔,xj-x拔)=cov(xi,xj)+cov(xi,-x拔)+cov(-x拔,xj)+cov(-x拔,-x拔)=cov(xi,xj)+cov(x拔,x拔)-2cov(xi,x拔)
=-cov(x1,x拔)-cov(xn,x拔)+cov(x拔,x拔)