Variable Selection Of EXP Type Group Based On Adjusted Rank Regression

Variable selection is an important topic in statistics.With the development of the society,the era of big data is here,and the power of variable selection is also apparent.The penalized least squares method with some appropriately defined penalty is widely used for simultaneously variable selection and coefficient estimation in linear regression.EXP penalty is an exponential type penalty which very closely resembles the L0 penalty.The EXP penalized least squares estimators are shown to have selection consistency and the asymptotic normality.However,the efficiency of least squares based penalization is adversely affected by outliers and heavy tailed distributions.To overcome this issue,the rank regression estimator is a useful and robust alternative method.In many regression problems,the explanatory factor may be represented by a group of input variables.The most common example is the multifactor analysis-of-variance problem,in which each factor may have several levels and can be expressed through a group of dummy variables.The EXP and rank regression methods can be used to select individual variables.There are no researches about group variable selection by combining these two methods.In this paper we consider regression problems with covariates having group structures.Our interest is in studying the adjusted regularized rank regression based on the EXP penalty for group variable selection.The specific research is divided into the following five chapters.Chapter one gives the research background and significance,the research status of the do-mestic and international.Chapter two introduces the linear models and the theory about the penalized least squares method.In chapter three,we present a new objective function about adjusted rank regression using the EXP penalty and discuss some theoretical prop-erties of adjusted rank regression estimator,and show the proofs of theoretical results.It provides theoretical basis for simulation and application.Chapter four conducts simulation studies based on the linear model.We compare the performance about group selection of three methods including adaptive Lasso based on rank regression,EXP penalty and our new method.To test the application of our method,a real data is analyzed.The results show that our method performs well in application.Chapter five is the summary of this paper.