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# Optimal multivariate linear model predictive

Author: HuangJieWu
Tutor: YuShengHua
School: Central South University
Course: Probability Theory and Mathematical Statistics
Keywords: Multivariate linear model Growth Curve Model Optimal linear prediction Best Linear Unbiased Prediction Best Linear Unbiased Prediction conditions Robustness
CLC: O224
Type: Master's thesis
Year: 2006
Quote: 0

### Abstract

 Multiple linear models are an important class of statistical models, has now become the natural sciences and social sciences fields indispensable tool for data analysis. Because of its wide applications, multivariate linear model studies have become very important and made a series of research results. In multivariate linear model for the study, an important aspect is to study the optimal multivariate linear model prediction. Literature there are many problems in this area have been studied, this paper explores the arbitrary rank multivariate linear model optimal linear predictor and the optimal homogeneous linear predictor, with linear constraints with arbitrary rank multivariate linear model with linear constraints of arbitrary rank growth curve model best linear unbiased prediction conditions, multiple linear model Ridge prediction and best linear unbiased prediction compared optimality problem, based on the amount of ridge estimation and classical optimal prediction Prediction amount of deviation matrix on the optimal discriminant problem, arbitrary rank growth curve model best linear unbiased prediction problems to the stability, improve the multivariate linear model of optimal prediction theories. The full text is constituted by the five chapters: The first chapter briefly describes the basic concepts of multivariate linear models and multivariate linear model Optimal Prediction Research and research results, as well as problems arise with this main work of this paper. It also briefly describes the research conducted on this issue have prior knowledge. Chapter II study of arbitrary rank multivariate linear model optimal linear prediction and optimal homogeneous linear prediction, and consider the linear constraints of arbitrary rank with multivariate linear model conditions optimal linear unbiased prediction. The third chapter in the general multivariate linear model for common biased forecast - Ridge prediction and best linear unbiased prediction of optimal discriminant discussed, and to estimate the optimal prediction based on the amount of ridge and classical predictor About deviation optimal discriminant matrix were discussed. Chapter IV of the general growth curve model the optimal linear prediction, best linear unbiased prediction, optimal homogeneous linear prediction, and consider an arbitrary rank general linear growth curve model constraints HB = 0 under the condition best linear unbiased prediction. Chapter V arbitrary rank growth curve model best linear unbiased prediction robustness discussed.

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