Three Kinds Of Estimation For Coefficients In The Growth Curve Model

The growth curve model is a class of generalized linear models,which is put forward by Wishart in 1938 when he studied the growth of between different groups of animals and plants.In recent decades,statistical scholars make a lot of researches about growth curve model parameter estimation.In dealing with the problems of parameter estimation of the matrix,the least squares estimate is widely used in the existing literature.But the growth curve model is a kind of multivariate linear model,which contains a large number of regression independent variable.So when the independent variable present linear relationship,that is to say,the design of the corresponding matrix presents complex collinearity.The accuracy of parameter estimation is poorer.Therefore,statistical scholars began to study biased estimate of growth curve model.This paper is based on the growth curve model,consider the model in the presence of multi-collinearity.The biased estimate of the parameters and excellent properties were discussed.The main contents are as follows:?1?On the basis of the generalized ridge estimators,in order to deal with the multi-collinearity,a new class of estimation ??K,d?=??₁????₂+K?-1??₁????₂+dI??,for the parameters in mixed-effect coefficient linear model is proposed.Under certain conditions,the new estimation is shown to be superior to the LS estimation and Ridge estimation,and the mean square error of the new estimation is litter than thes estima-tions.?2?This paper discus the general liu estimates in a growth curve model.Although the covariance of the least square estimate is the smallest in linear unbiased estimation,the value is very big,under the condition that one of the design matrixes at least is ill-conditioned.In this case,the estimation accuracy becomes very poor and quite unstable.So it is necessary for us to make some improvement for design matrixes.Based on the least square estimate,this paper puts forward the general liu estimates and proves that this estimate is superior to the least square estimate and bridge estimate.?3?Given in the case of biased estimate deviates from its true value,this paper gives almost unbiased general liu estimates,integrating the concept of almost unbiased.This paper studies the properties of the estimation and give the optimal benign relative to the least square estimate and general Liu estimates.