Statistics and Its Interface

Volume 17 (2024)

Number 1

Special issue in honor of Professor Lincheng Zhao

Asymptotic properties of relative error estimation for accelerated failure time model with divergent number of parameters

Pages: 107 – 125

DOI: https://dx.doi.org/10.4310/23-SII816

Authors

Fei Ye (School of Statistics, Capital University of Economics and Business, Beijing, China)

Hongyi Zhou (Department of Mathematics, Tsinghua University, Beijing, China)

Ying Yang (Department of Mathematics, Tsinghua University, Beijing, China)

Abstract

The paper considers the problem of parameter estimation in the accelerated failure time model with divergent number of parameters under fixed design. We propose an estimator based on the general relative error criterion. We show that the proposed estimator is consistent and asymptotically normal under mild regular conditions. We also propose a variable selection procedure and show its oracle property as well as the consistency of model selection. Numerical studies have been conducted to compare the performance of different general relative error based estimators.

Keywords

general relative error, accelerated failure time model, divergent number of parameters, variable selection

2010 Mathematics Subject Classification

Primary 62F12. Secondary 62J99.

Received 15 November 2022

Accepted 15 August 2023

Published 27 November 2023