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

  • Joseph Nzabanita Linköping University, Sweden; National University of Rwanda, Rwanda
  • Dietrich von Rosen Swedish University of Agricultural Sciences, Sweden
  • Martin Singull Linköping University, Sweden
Keywords: extended growth curve model, estimation, linearly structured covariance matrix, residuals

Abstract

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.

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Published
2020-09-25
Section
Articles