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Estimation and Prediction of Generalized Growth Curve with Grouping Variances in AR( q ) Dependence Structure
Author(s) -
Lee Jack C.,
Hsu YingLin
Publication year - 2003
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200390003
Subject(s) - mathematics , autoregressive model , covariance matrix , statistics , growth curve (statistics) , covariance , matrix (chemical analysis) , diagonal , transformation (genetics) , estimation theory , function (biology) , biochemistry , chemistry , gene , evolutionary biology , biology , materials science , geometry , composite material
Abstract 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 Σ = D σ CD 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 < ρ < 1 and σ l , l = 1, …, g , are unknown. We consider both parameter estimation and prediction of future values. Results are illustrated with real and simulated data.