Prediction intervals for growth curves

The growth curve model Y^n×p = A^{n×p ξ mtimes;k}B^k×p+ E^nxp, where Y is an observation matrix, &sigma is a matrix of unknown parameters, A is a known matrix of rank m, B is a known matrix of rank k with 1'= (1, …, 1) as its first row, and the rows of E are independent each distributed as N^p(0,Σ,) is considered. The problem of constructing the prediction intervals for future observations using the above model is considered and approximate intervals assuming different structures on σ are derived. The results are illustrated with several data sets.