Multivariate Linear Model The Optimal Forecast

Multivariate linear model is a branch of important statistical model. Now it has become an indispensable tool for data analysis in every field of natural science and social science. Because of its comprehensive application in many fields, the study of the multivariate linear model is becoming more important and many researchers have obtained some excellent achievements. In this paper we study the optimal linear predication and the optimal uniform linear predication in the multivariate linear model with arbitrary rank, we consider the conditional optimal linear unbiased predication in the multivariate linear model with arbitrary rank and the growth curve model with arbitrary rank.We investigate the optimality distinguish of the shrinked predication and the optimal linear unbiased predication in the multivariate linear model.Robustness of the optimal linear unbiased predication in the growth curve model are investigated .This thesis consists of five parts as following:In the first chapter,we introduces some basic concepts and theorems on multivariate linear model and the research status ,and the origin of the problem we discussed.And the main works of this paper are also simply introduced.In the second chapter,we study the multivariate linear model with arbitrary rank.We obtain the optimal linear predication, the optimal uniform linear predication and the conditional optimal linear unbiased predication.In the third chapter, we investigate the optimality distinguish of the shrinked predication and the optimal linear unbiased predication in the multivariate linear model.In the fourth chapter,we study the the growth curve model. the optimal linear predication, the optimal linear unbiased predication and the optimal linear unbiased predication are obtained .we investigate the conditional optimal linear unbiased predication in the growth curve model with arbitrary rank.In the fifth chapter robustness of the optimal linear unbiased predication in the growth curve model are investigated. Necessary and sufficient conditions for the predictor of linear predictable variable to be robust with respect to covariance matrices are obtained.