Research On Weighted Mixed Ridge Estimator And Liu-Type Estimator In Singular Linear Model

Linear models are the important model in modern statistics and play a central partin modern statistics. In this dissertation, we mainly focus on the estimation of parameterwith stochastic restrictions. We also research the singular linear model with equalityrestrictions.In the linear model with stochastic linear restrictions, considering to combiningestimator is an efficient method to overcome multicollinearity problems. Based on this,a new weighted mixed ridge estimator was proposed. Necessary and sufficientconditions for the superiority of the proposed estimator over the generalized leastsquares estimator、the ridge estimator and the weighted mixed estimator in the meansquared error matrix criterion are obtained. And a numerical example is also given toshow the theoretical results.Considering the singular linear model, this article concerned with the regressionparameter in singular linear model with linear equality restrictions. In order to overcomemulticollinearity in regression model, a new Liu-Type estimator is proposed. Someproperties are also studied. Necessary and sufficient condition for the new Liu-Typeestimator is superior to the restricted linear squares estimator in the mean squares errormatrix(MSEM) criterion is given; We also show a sufficient condition for the newLiu-Type estimator superiority of the restricted least squares estimator in terms of meansquares error(MSE) criterion.