Separation Of Covariates In Partially Linear Single-index Proportional Hazards Regression Models

Partial linear single-index proportional hazards models play an important role in the fields of sociology and clinical medicine.However,previous studies on thesemodels were based on the condition that the structure of the models are known.A subjective determination of the models structure whether the covariate has a linear effect or not challenges the rationality of the models' structure,which is based on the background knowledge of the research or some imple descriptive data analyses for each covariate.Therefore this paper mainly studies the problems of the structure identification and parameter estimation in some linear single-index proportional hazards regression models.In this paper,we study the problem of the structural identification in partial linear single-index proportional hazards model based on B-spline approximation non-concave penalty partial likelihood method.In order to achieve the identifiability of the model structure,we assume that the linear and index parts contain all the covariates and impose constraints on the parameters.Firstly,B-spline approximation technique is applied to the single index function.Then,under the condition of recognizability constraints,the logarithm partial likelihood function is maximized and the estimation of B-spline coefficient,index parameters and linear parameters and model selection can be achieved reaching the purpose of model sparse variable selection and structure identification.Finally,the effectiveness of the proposed method is verified by data simulation examples.