Robust Adaptive Group Penalty Estimation Under Accelerated Failure Time Models

With the advent of the information age,the influx of massive information makes data show explosive growth.Any tiny data may produce incredible results.Vari-able selection is the most important method of data processing.Traditional vari-able selection methods do not have the excellent performance of processing high-dimensional data,A new method of introducing a penalized function to select and estimate parameters was produced.The appearance of the classic penalized variable selection method Lasso in 1996 is a breakthrough development.The central idea is to compress the coefficients,unfortunately,it does not have the oracle property.Some statisticians try to add weights to the penalty item to improve the performance of Lasso.In addition,data often have outliers and have a group structure in actual problems.The group variable selection method based on the penalized idea came out,it can establish a robust model which has simple structure,easy-to-interpret parameters and high accuracy.This article mainly studies the problem of robust group variable selection based on the AFT model(Accelerated Failure Time Model).When there are heavy-tailed errors or outliers in the survival data,the LAD(Least Absolute Deviation)regression is used to estimate unknown parameters,combining with the group variable penalty method,the AGPWLAD(Adaptive Group Penalized WLAD)method is proposed to achieve robust group variable selection of parameters.Theoretically,we prove that this method has enjoy the consistency of group variable selection and the asymptotic normality of parameter estimation.In application,we improve the existing method,give numerical simulation results and obtain better numerical analysis results.We apply the proposed method in this paper to the data of primary biliary cirrhosis,finally,the analysis results show that the proposed method performs well.The structure of this article is as follows:The chapter 1 introduces the relevant basic knowledge of the Cox proportional hazard model,the AFT model and related research status.The chapter 2 introduces penalized variable selection,penalized group variable selection and the literature of these two types of methods,respec-tively.Chapter 3 is the main part of this article,we use Kaplan-Meier weights to deal with the censoring problem,We propose the objective function of AGP-WLAD estimation in the AFT model.Under general conditions,the consistency of the estimator is obtained.In addition,by appropriately selecting the adjusted parameters,the estimators have the oracle property.The results show that the AGPWLAD method based on the AFT model can complete group selection and pa-rameter estimation simultaneously.Chapter 4 presents the algorithm for calculating the AGPWLAD estimation and the choice of tuning parameters.Under different censoring ratios and error distributions,this algorithm is used to complete the op-timization,and good simulation results have been obtained.The real data analysis shows the practicability of this method.Chapter 5 summarizes the research of this article.