More Research On The Biased Estimation In The Semiparametric Regression Model

The semi-parametric model contains two parts: one is the parametric part, the other one is the non-parametric part which means the semiparametric model has the advantages of the linear model and the non-parametric model. And the interpretation of dealing with the practical problems is much more persuasive. Then there are lots of researchers attracted to study the semi-parametric model, and also the semi-parametric model has been widely used in the administrative, economic, financial, biological, medicinal, meteorologic and environmental science, engineering, agricultural and industrial and other fields.In these lots of research results, it has been basically formed a relatively complete theoretical system. For the semiparametric linear model, there are many methods to estimate the parametric part and the non-parametric part, and the most important methods are the penalized least squres method, the two stages estimate, the kernel smoothing method, the robust estimate and so on.But there widely is a phenomenon in the actual problem-problem of multicollinnearity, also called ill-conditioned design matrix. So we use the classic least squared method to estimate the parametric part in the front mothods, while the classic least squares method is inadequate in dealing with the problem. In linear regression model,there are many scholars having made effort to sovle the problem, but in the semi-parametric model, it is not enough. it is well known that the biased estimation is a good way to combat the problem. Many results of the biased estimation have been widely used, the most importamt biased estimators are Stein Shrinkage Estimator, Principal Components Estimator, Ridge Estimator, Liu Estimator and so on. And maybe these biased estimstors also can been used in the semi-parametric model to estimate the parametric part. So in this paper,the tasksare as the follows:For semiparametric linear regression model, the commonly used methods are the penalized least squres method, the two stages estimate, the kernel smoothing method, the robust estimate. In tihis paper, we consider difference method to study semiparametric linear regression model. Since the unbiasedness is an important statistical property. So we consider a difference based almost unbiased ridge regression estimator and a difference based almost unbiased Liu regression estimator. Both of the two estimators are analysed and compared in the sense of mean squared error. And then we give the result that either of the difference based almost unbiased ridge regression estimator and the difference based almost unbiased Liu regression estimator is superior to the difference based ridge regression estimator and the difference based Liu regression estimator and the classic least squared estimator, respectively. After that, we illustrate the performance of the estimators with a Monte Carlo experiment and an application.For the difference based ridge regression estimator, it has a very worth studying problem that is the selection of ridge parameter. At the last part, we consider a Monte Carlo experiment for the selection of ridge parameter. And at different rules,we get the rules how to choose the ridge parameter estimate methods at different cases.