A New Almost Unbiased Liu-type Estimator

As one of the important research directions of modern statistics,linear model has been widely used in various fields.However,the existence of multicollinearity between the explanatory variables of the data leads to the "ill condition" of the design matrix.then,the performance of the least squares estimator is no longer satisfactory.Biased estimator improves the least squares estimator and can solve this problem well,but the deviation between biased estimator and true value of parameter will affect the accuracy of estimation.Therefore,in this thesis,we mainly study the biased estimator of parameters in linear model,and obtain a new almost unbiased Liu-type estimator,then discuss its related statistical properties and advantages.Considering the general linear regression model,with the idea of almost unbiased estimator,we obtain a new almost unbiased Liu-type estimator based on the new Liu-type estimator and give the concrete form of the new estimator.Then,we study the statistical properties of the new estimator,including bias,variance and mean square error.Next,the sufficient conditions for the superiority of the new estimator over the least squares estimator and the new Liu-type estimator are discussed under the mean square error criterion,and the parameter selection method for the new estimator is given.In the meantime,the theoretical results are illustrated by Monte Carlo simulation and numerical example analysis.In addition,we also study the superiority of the new estimator and the least squares estimator under the Pitman criterion,and give the sufficient condition for the superiority of the new estimator over the least squares estimator.In order to prove the superiority of the new estimator in the sense of mean square error,we compare the new estimator with the almost unbiased ridge estimator,the almost unbiased Liu estimator and the almost unbiased two parameter estimator under the mean square error criterion,and obtain the sufficient conditions for the superiority of the new estimator over these three almost unbiased estimators.Next,the Monte Carlo simulation and numerical example analysis further demonstrate that under certain conditions,the new estimator performs better than these three estimators in both theoretical research and practical application.