Shrinkage Estimation in Sparse Partially Linear Models with Right-censored Data

Abstract

This study focuses on the estimation of sparse partially linear models in the presence of right-censored data. A synthetic data transformation is employed to address censoring, while regression coefficients are partitioned to achieve sparsity. The proposed methodology introduces modified shrinkage and pretest estimators, achieved by integrating synthetic data and partitioning techniques. The estimation of the nonparametric component is conducted using smoothing splines. These estimators synthesize synthetic data transformation, smoothing splines, and shrinkage strategies. Comprehensive theoretical explanations and the asymptotic properties of the estimators are presented. Simulation studies, alongside an analysis of a hepatocellular carcinoma dataset, are utilized to demonstrate the approach's efficacy. Additionally, performance is assessed under high-dimensional data settings (p > n) through simulation and evaluation on the Norway/Stanford Breast Cancer dataset. The findings indicate that the proposed shrinkage and pretest estimators surpass submodel estimation for both low and high-dimensional data under conditions of right-censoring.