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Estimation for an additive growth curve model with orthogonal design matrices

An additive growth curve model with orthogonal design matrices is proposed in which observations may have different profile forms. The proposed model allows us to fit data and then estimate parameters in a more parsimonious way than the traditional growth curve model. Two-stage generalized least-squares estimators for the regression coefficients are derived where a quadratic estimator for the covariance of observations is taken as the first-stage estimator. Consistency, asymptotic normality and asymptotic independence of these estimators are investigated. Simulation studies and a numerical example are given to illustrate the efficiency and parsimony of the proposed model for model specifications in the sense of minimizing Akaike's information criterion (AIC).