Multistage regression model

summary:Necessary and sufficient conditions are given under which the best linear unbiased estimator (BLUE) $\hat{\beta}_i(Y_1,\dots, Y_i)$ is identical with the BLUE $\hat{\beta}_i(\hat{\beta}_1,\dots, \hat{\beta}_{i-1}, Y_i)$; $Y_1\dots, Y_i$ are subvectors of the random vector $Y$ in a general regression model $(Y, X\beta,\sum)$, $(\beta'_1,\dots,\beta'_i)'=\beta$ a vector of unknown parameters; the design matrix $X$ having a special so called multistage struture and the covariance matrix $\sum$ are given