In the linear epoch regression model $E(Y^{(j,j)}=E \left(\matrix Y_1^{(1)}\\ \vdots\\Y_j^{(j)} \endmatrix\right)=\left(\matrix X_{11}, & X_{21}, & 0, & \dots, & 0\\X_{12}, & 0, & X_{22}, & \dots, & 0\\\vdots & \vdots & \vdots & \ddots & \vdots \\ X_{1j}, & 0, & 0, & \dots & X_{2j} \endmatrix\right)\left(\matrix \beta_1\\ \beta_{21}\\ \vdots\\ \beta_{2j} \endmatrix\right)$, $\text{var}\left(Y^{(j,j)\right)= \left(\matrix \sum^{p1}_{s1}\vartheta_{1_{s1}}H_{1_{s1}}, & \dots , & 0\\ \vdots & \ddots & \vdots\\ 0, & \dots, & \sum^{p_j}_{s_j}\vartheta_{js_j}H_{js_j} \endmatrix \right)$ the locally best linear unbiased estimators of the first order parameters and the locallz minimum variance quadratic unbiased and invariant estimators of an unbiasedly and invariantly estimable linear function of the second order parameters in the $jth$ epoch and after the $jth$ epoch are derived. The algorithms mentioned utilize the special block structure of the model and the sparseness of the covariance matrix of the observation vector.
@article{104487,
author = {Ludmila Kub\'a\v ckov\'a},
title = {The locally best estimators of the first and second order parameters in epoch regression models},
journal = {Applications of Mathematics},
volume = {37},
year = {1992},
pages = {1-12},
zbl = {0743.62057},
mrnumber = {1152153},
language = {en},
url = {http://dml.mathdoc.fr/item/104487}
}
Kubáčková, Ludmila. The locally best estimators of the first and second order parameters in epoch regression models. Applications of Mathematics, Tome 37 (1992) pp. 1-12. http://gdmltest.u-ga.fr/item/104487/
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