The Discussion Of Asymptotic Properties In High Dimension Linear Regression With Adaptive Lp Regularization

In linear regression, both variable selection and estimation can be completed if there are some kinds of regularization. Normally, we evaluate the estimator with so called "oracle property". This paper will discuss the performance of estimator in linear regression with adaptive Lp regularization (0< p< 1). When the number of variable is fixed, oracle property has been proved. In this paper, The number of variable is not fixed. And we will give the specific condition and prove the oracle property of adaptive Lp regularization estimator when sample size and variable number both go to infinity. Meanwhile, the algorithm for adaptive Lp regularization will be proposed through quadratic programming and the simulation will give comparison with Lasso, adaptive lasso, Lp regularization, adaptive Lp regularization and OLS.