Variable Selection Mothod In Several Regression Models

The main function of the variable selection method is to choose the appropriate useful variable to reduce the dimension so as to establish a simple model. The Dantzig selector (DS) and its related methods are new high dimensional data variable selection method for data structure which dimension is greater than that of sample. It can achieve the variable selection and parameter estimation together. In this thesis, we study the characterization and applications of the DS and adaptive dantzig selector (ADS) in several statistical models, the main research we have carried on and their results are as follows:(1) According to the common counting variable, we put forward variable selection and parametric estimation for the Poisson logarithm linearity model via the DS and ADS. Emphasize focus on the asymptotic property of ADS under the Poisson log-linear model. Prove the asymptotic normality of nonzero coefficient estimated in ADS estimator, and the accurate identification of zero coefficients. That is, ADS method under Poisson log-linear model has the oracle properties. Finally, we carry on the instance analysis to test that whether the ADS is superior to the adaptive lasso (ALasso) under Poisson log-linear model.(2) In addition to the count variable, dichotomous variable is also very common. We put forward logistic regression model via the DS and ADS to study the variable selection problem with the dichotomous variable as the response. We obtain that the ADS estimator for the logistic regression model has the oracle properties under some appropriate conditions. In addition, a numerical simulation is made to check the feasibility and the effectiveness. Finally, we find a better solution of performance comprehensive evaluation analysis in life insurance companies by using ADS of the logistic regression model combining with the projection pursuit method.(3) For the ADS, we focus on its asymptotic properties in Semi-parameter model. We obtain that the ADS estimator for the Semi-parameter model has the oracle properties under some appropriate conditions no matter the number of explanatory variables grows in a polynomial rate or in an exponential rate. Finally, we carry on a simulation study and draw a conclusion that the ADS method is more applicable and feasible than lasso and other variable selection methods.