Estimator Of Regression Coefficients In The Growth Curve Model

In this paper, some researches on estimator of parameters in the growth curve model are considered.To estimate the regression coefficients B, we proposed the new root power estimator, local root power estimator and ridge estimator which is based on the decomposition of singular value. Discuss their superiority over LSE.In Chapter 2, we introduce the new root power estimator of regression coefficients B when the design matrix present ill-condition. It is proved that by choosing the proper parameters, the new estimator is better than LSE and the normal root estimator under MSE criterion. Prove it's admissibility. Two methods of choosing the new root power parameters are introduced.In Chapter 3,we consider the local root power estimator. Prove its superiority over LSE under MSE criterion and PC criterion. Give two methods of choosing the local root power parameters.In Chapter 4,we combine the decomposition of singular value and ridge estimator. Introduce the ridge estimator based on the decomposition of singular value. Discuss its superiority over LSE under MSE, MSEM and PC criterion.In Chapter 5,Use the logarithmic derivative formula of Г function, analysis the characters of X2distributed density function in detail, and the effects of change of the parameter on density curve. Points out the properties of maximum value of X~2 distributed density function, and the relation of different X~2 distributed density function according to different parameters. Analysis the properties of intersection point of two density curves,Gains the differential equation about X~2 distributed density curve by above analysis.