Underparametrization in a regression model with constraints II

Lubomír Kubáček

Multistage regression model

Lubomír Kubáček (1986)

Aplikace matematiky

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

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