Statistics and Its Interface

Volume 14 (2021)

Number 4

Group variable selection for recurrent event model with a diverging number of covariates

Pages: 431 – 447

DOI: https://dx.doi.org/10.4310/21-SII663

Authors

Kaida Cai (Department of Mathematics and Statistics, University of Calgary, Alberta, Canada)

Hua Shen (Department of Mathematics and Statistics, University of Calgary, Alberta, Canada)

Xuewen Lu (Department of Mathematics and Statistics, University of Calgary, Alberta, Canada)

Abstract

For the high-dimensional data, the number of covariates can be large and diverge with the sample size. In this work, we propose an adaptive bi-level penalized method to solve the group variable selection problem for the recurrent event model with a diverging number of covariates. Comparing with the classical group variable selection methods, the adaptive bi-level penalized method can select the important group variables and individual variables simultaneously. For the case of diverging a number of covariates, we demonstrate that the proposed method has selection consistency and the penalized estimators have asymptotic normality. Simulation studies show that the proposed method performs well and the results are consistent with the theoretical properties. The proposed method is illustrated by analyzing a real life data set.

Keywords

group variable selection, recurrent event model, adaptive bi-level penalty, diverging dimension, asymptotic normality, oracle property

2010 Mathematics Subject Classification

Primary 62J07. Secondary 62F12, 62N01, 62P10.

Received 12 April 2020

Accepted 29 January 2021

Published 8 July 2021