Statistical inference for parallelism hypothesis in growth curve model

Source abstract

Let y=(y1,…,yp)′ be a p-dimensional random vector measurable on the individuals drawn from each of k p-dimensional normal populations ∏i:Np(μi,Σ), i=1,…,k. In this paper we consider the growth curve model which has a mean structure as follows: μi=Xθi,i=1,…,k, where X is a p×q given matrix with rank q and θi’s are unknown parameter vectors. First we derive an LR test for a parallelism hypothesis H1:Xθi−Xθk=γi1p, i=1,…,k−1, where γi’s are unknown parameters, and 1p is the p-dimensional vector with all the elements 1. Next we obtain the MLE of γ=(γ1,…,γk−1)′ and its distribution, and propose a simultaneous confidence interval for linear combinations of γ.