The Property Of Bayes Linear Unbiased Estimator Of Growth Curve Model

As a very useful mathematical tool,Growth Curve Model can help us to study so many problems.Because of its wide range applications in architecture,mechanism,medicine,manufacture,transportation,psychology,economics and other fields,more and more statisticians research this model increasingly deeply.In this paper,we mainly study the parameter estimation problem of Growth Curve Model.Maney scholars have made a lot of research about the parameter estimation problem of this model,such as least squares estimate,the Bayes linear unbiased estimation,the generalized Liu estimates that almost unbiased generalized ridge estimation,combinatorial biased estimate,and many other estimate forms.Because that the Growth Curve Model is a kind of multivariate linear model,there will contains a large number of linear correlation regression independent variables.When the design of the corresponding matrix presents complex collinearity,we cannot guarantee the accuracy of parameter estimation which will appear lot of deviation.Therefore,people begin to focus on the biased estimation and almost unbiased estimation of Growth Curve Model.This paper will introduce almost unbiased Liu estimates,almost unbiased ridge estimation and the Bayes linear unbiased estimation.Moreover,we will compare the optimal benign of them based on mean square error estimates?Following is the detail.The first chapter will introduce the domestic and international research progress and application of growth curve model.The second chapter wil introduce some elementary knowledge.The third chapter will introduce the property of Bayes linear unbiased estimator.