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Keywords:
mixed linear model; necessary and sufficient conditions; best linear unbiased estimator; BLUE; multistage structure; regression model
mixed linear model; necessary and sufficient conditions; best linear unbiased estimator; BLUE; multistage structure; 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.
References:
[1] Lubomír Kubáček: Efficient estimates of points in a net constructed in stages. Studia geoph. et geod. 15, 1971, 246-253.
[2] Lubomír Kubáček: Locally best quadratic estimators. Math. Slovaca 35, 1985, 393 - 408. MR 0820638
[3] C. R. Rao: Linear Statistical Inference and Its Applications. J. Wiley, N. York 1965. MR 0221616 | Zbl 0137.36203
[4] С. R. Rao S. K. Mitra: Generalized Inverse of Matrices and Its Applications. J. Wiley, N. York 1971. MR 0338013
[5] Júlia Volaufová: Estimation of mean and variance in two-stage linear models. (To appear in Aplikace matematiky.)
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