Further Study On Some Problems Of Biased Estimation

Linear models are especially important statistical models, including linear regression model, variance and analysis, covariance and analysis, and variance and component one etc.. This thesis mainly considers ordinary linear regression model and generalized one, that is, models and are involved. In term of the unknown parameter , it is necessary to study its estimation. Based on the least squares and biased estimation especially ridge estimation, a new estimation, that is, generalized ridge estimation is put forward through studies on restriction of the parameter . Model's prediction being considered, comparison of superiority of optimal and classical predictions with respect to the ridge estimation is showed. Regression diagnoses especially distance for principal components estimation is discussed. The main results are as follows:According to the approximate multicollinearity of matrix , the third chapter constrains the regression coefficient and obtains generalized ridge estimation of the linear model's parameter under the ellipsoidal restriction. Then discusses its properties, such as biased property, relative efficiency of generalized variance and superiority comparisons between generalized ridge estimation and generalized least squares estimation. Shows iterative algorithm based on the mean dispersion error. In term of the prediction problem, the fourth chapter discusses its superiority of the optimal and classical predictors based on the ridge estimation, and gives an necessary and sufficient condition of comparison of its superiority under the condition of criterion by some properties of partial ordering of matrix. Thus proposes an alternative method for the research of superiority of two predictors based on the biased estimation.In the light of the approximate multicollinearity of matrix, distance for principal components estimation (namely distance) is put forward. Deletion is employed and the exact deletion formula for distance is gained, which not only simplifies the computation but also proposes a diagnostic for identifying influential observations.