Previous |  Up |  Next


Title: The locally best estimators of the first and second order parameters in epoch regression models (English)
Author: Kubáčková, Ludmila
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 37
Issue: 1
Year: 1992
Pages: 1-12
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: regression linear model
Keyword: epoch model
Keyword: linear epoch regression model
Keyword: locally best linear unbiased estimators
Keyword: first order parameters
Keyword: locally minimum variance quadratic unbiased and invariant estimators
Keyword: estimable linear function
Keyword: second order parameters
Keyword: algorithms
Keyword: block structure
Keyword: sparseness of the covariance matrix
MSC: 62H12
MSC: 62J05
MSC: 62J10
MSC: 65C99
idZBL: Zbl 0743.62057
idMR: MR1152153
DOI: 10.21136/AM.1992.104487
Date available: 2008-05-20T18:42:51Z
Last updated: 2020-07-28
Stable URL:
Reference: [1a] Lubomír Kubáček: Foundations of Estimation Theory.Elsevier, Amsterdam, Oxford, New York, Tokyo, 1988. MR 0995671
Reference: [2a] Lubomír Kubáček: Special structures of mixed linear model with nuisance parameters.Math. Slovaca 40 (1990), 191-207. MR 1094773


Files Size Format View
AplMat_37-1992-1_1.pdf 1.225Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo