Ridge And Principal Correlation Estimation In Parameter Of Linear Regression Model

This thesis focuses on the respective advantages of ridge and principal correlationestimation under constraints and without constraints in linear regression model. Since theadvancement of mean squared error, parameter estimation in linear regression model hasbeen one of the focuses in the research of statistics. Although Markov has proved theminimum value of squared error of the least square estimation among linear unbiasedestimations, statisticians have come to recognize the inadequacy of least square estimationwhile applied to multicollinearity and advanced biased estimations, ridge and principalcorrelation being two of the most commonly applied. All these biased estimations undersquare loss function have advantages over the least square estimation. This paper developsas follows:Beginning with ridge and principal component estimation, the author introduces ridgeand principal correlation estimation, thereby proving it to be linear transformation of theleast square estimation and its compressibility and bias, expounding the advantages of theestimation under mean squared error matrix. After that this estimation's admissibilityunder quadratic loss function is discussed, the values of ridge parameter are established,and the validity of the estimation is proved with experiments.From the linear model's parameter under constraints the author goes to ridge andprincipal correlation estimation, proving the fact that, under linear constraints, generalizedmean square error of ridge and principal correlation estimation is smaller than that of leastsquare estimation.The following is to expand the ridge and principal correlation estimation intogeneralized ridge and principal correlation estimation, proving its admissibility underquadratic loss function and furthering to generalized ridge and principal correlationestimation under constraints. Finally this thesis attributes hypothesis testing of linearmodel to parameter estimation under linear constraints, leading to F test statistic of ridgeand principal correlation estimation.