Estimation and Prediction of Generalized Growth Curve with Grouping Variances in AR(q) Dependence Structure

摘要

In this paper we consider maximum likelihood analysis of generalized growth curve model with the Box-Cox transformation when the covariance matrix has AR(q) dependence structure with grouping variances. The covariance matrix under consideration is ∑ = D_σCD_σ where C is the correlation matrix with stationary autoregression process of order q, q < p and D_σ is a diagonal matrix with p elements divided into g(≤p) groups, i.e., D_σ is a function of {σ_1,...,σ_g} and -1 < p < 1 and σ_1, l = 1,...,g, are unknown, We consider both parameter estimation and prediction of future values. Results are illustrated with real and simulated data.