scholarly journals Admissibility of linear predictor in the extended growth curve model

2020 ◽  
Vol 15 (1) ◽  
pp. 15-26
Author(s):  
Zhihong Xiao ◽  
Qiang Zhu
Keyword(s):  
Growth Curve ◽  
Sufficient Conditions ◽  
Growth Curve Model ◽  
Linear Predictor ◽  
Matrix Properties ◽  
Curve Model ◽  
Extended Growth Curve Model ◽  
Linear Predictors ◽  
Definition Of ◽  
Necessary And Sufficient

In the present paper, we first give the definition of the extended growth curve model, then according to the definition of admissible linear predictor and some matrix properties, obtain the necessary and sufficient conditions for a linear predictor to be admissible in the classes of homogenous and inhomogeneous linear predictors, respectively.

scholarly journals Estimation of parameters in the extended growth curve model with a linearly structured covariance matrix

2012 ◽  
Vol 16 (1) ◽  
pp. 13-32
Author(s):  
Joseph Nzabanita ◽  
Dietrich von Rosen ◽  
Martin Singull
Keyword(s):  
Covariance Matrix ◽  
Growth Curve ◽  
Estimation Procedure ◽  
Inner Product ◽  
Dispersion Matrix ◽  
Growth Curve Model ◽  
Estimation Of Parameters ◽  
Curve Model ◽  
Extended Growth Curve Model ◽  
Residual Space

In this paper the extended growth curve model with two terms and a linearly structured covariance matrix is considered. We propose an estimation procedure that handles linearly structured covariance matrices. The idea is first to estimate the covariance matrix when finding the inner product in a regression space and thereafter re-estimate it when it should be interpreted as a dispersion matrix. This idea is exploited by decomposing the residual space, the orthogonal complement to the design space, into three orthogonal subspaces. Studying residuals obtained from projections of observations on these subspaces yields explicit consistent estimators of the covariance matrix. An explicit consistent estimator of the mean is also proposed and numerical examples are given.

Residuals in the Extended Growth Curve Model

2006 ◽  
Vol 33 (1) ◽  
pp. 121-138 ◽  
Author(s):  
JEMILA SEID HAMID ◽  
DIETRICH VON ROSEN
Keyword(s):  
Growth Curve ◽  
Growth Curve Model ◽  
Curve Model ◽  
Extended Growth Curve Model
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