Statistical inference for parallelism hypothesis in growth curve model

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(i , ), i = 1, . . ., k.In this paper we consider the growth curve model which has a mean structure as follows:i = X"i, i = 1, . . ., k, where X is a p q given matrix with rank q and "i's are unknown parameter vectors.First we derive an LR test for a parallelism hypothesis H1 : X"i -X" k = i1p, i = 1, . . ., k -1, where i's are unknown parameters, and 1p is the p-dimensional vector with all the elements 1.Next we obtain the MLE of = (1, . . ., k-1 ) and its distribution, and propose a simultaneous confidence interval for linear combinations of .