Compare The Difference Based Estimation And SCAD For Partially Linear Regression Model And Research On Nonnegative Variable Selection With Outliers

Variable selection plays a more and more important role in modern statistics. The LASSO method proposed Tibshirani has been a great concern In recent years. The penalty functions in LASSO method have been used in a variety of models to solve practical problems. This study is divided into two parts: Firstly, compare the differential estimators nd SCAD in partial linear regression model, mainly in order to study the performance of variable selection in other more complicated models and to study the advantages and disadvantages of the estimators. Secondly, this paper discusse the applications of penalty function in Linear model with some complex data sets. This article apply the penalty function applied to the data sets with the outliers, and mainly make deep research from two aspects of variable selection.(1) SCAD and Improved difference based estimation for partial linear regression models: we propose the shrinkage difference based estimators with better performances. A shrinkage estimator combines the corresponding unrestricted estimator and restricted estimator when the validity of the prior restrictions are suspected. We also develop the properties of these estimators using the notion of asymptotic distributional risk. The shrinkage estimators are shown to have higher efficiency than traditional the difference based estimator. Further, we consider a Smoothly Clipped Absolute Deviation Penalty(SCAD) type estimation strategy and compare the relative performances with the shrinkage difference based estimators through a Monte Carlo simulation study. For the nonparametric component, the local polynomial technique is implemented. We also compare four local polynomial estimators in which the parametric components are estimated by shrinkage and SCAD strategies. An example of application is also illustrated.(2) Research on nonnegative variable selection with outliers under Linear model: This section introduced the properties of SROS:(a) the SROS is nearly regression equivariant;(b) the SROS estimator has the same breakdown value of ROS estimator, and the ROS estimator has the maximum breakdown value.Our non-nagative SROS and non-nagative irrepresentable condition with outliers are proposed in the paper.We prove that the non-nagative SROS has variable selection consistency. In simulation part,we compare the MSE of LTS,ROS,LAD-lasso,SROS and non-negative SROS in three models with different data sets.We can see that our new estimators permfomance very well and these parameter values estimated by our methods are the most close to the true value.The comparetions will be shown in some tables latter.