Independence Screening In Sparse Ultra-High-Dimensional Linear Transformation Model

Linear transformation model is a class of survival analysis model which is very flexible and contains many commonly survival analysis models,such as Cox propor-tional hazards model,proportional odds model and probit model.Along with the de-velopment of technology and the increasing ability to gather and store data,high di-mensional,even ultra-high dimensional data emerges constantly.This is a challenge to the statistical inference of the traditional model.Because of this,the paper will discuss the problem of variable selection and parameter estimation with ultra-high dimensional linear transformation model.Based on the maximum likelihood estimation method,we usually firstly decrease the size of variables to a moderate size(p<n)and then perform models selection and coefficients estimation.Then we will discuss variable selection in the linear transforma-tion model using sure independence screening(SIS).Finally,we extand SIS to iterated sure independence screening(ISIS).For variable selection problem,ISIS is a more effective method.At the last of this paper,we will give a large number of simulation examples to show the effectiveness of the method.