Independence Screening In Sparse Ultra-High-Dimensional Varying Coefficient Transformation Model

Varying coefficient transformation model has played an increasingly important role in statistical analysis,it is widely used in clinical trials and biomedical studies.Along with the development of technology and the increasing ability to gather and store data,high dimensional,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 varying coefficient transformation model.At first,the paper talks about some common methods about ultra-high-dimensional reduction,then 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.As for ultra-high-dimensional situations,we talk about variable selection in the varying coefficient transformation model by sure independence screening(SIS).Then,the paper extends SIS to iterated sure independence screening(ISIS).For variable selection of this model,ISIS method is more effective.At last,we will give a large number of simulation examples to show the effectiveness of the method.