Model-based recursive partitioning algorithm to penalized non-crossing multiple quantile regression for the right-censored data

Abstract

Quantile functions of the response variable provide a tool for practitioners to analyze both the central tendency and statistical dispersion of data. As a counterpart to the regression tree models, quantile regression tree methods (QRT) gained interest in constructing tree models for quantile functions. Previous QRT methods, however, estimate different tree models for each quantile level as they separately estimate QRT models. To The unified non-crossing multiple quantile regression tree (UNQRT) model was proposed to construct a common tree structure by aggregating information across all quantile levels. UNQRT, however, does not benefit from automatic variable selection techniques developed in regression literature. We propose a penalized UNQRT (P-UNQRT) method by incorporating adaptive sup-norm penalty into the original UNQRT model to perform variable selection. Additionally, we extend P-UNQRT to cope with the right-censored data that often arise in healthcare applications. The Kaplan-Meier estimator is used as weights for each observation of the censored data in our proposed model. We demonstrate the benefits of our algorithms through empirical studies and analyze the military training data from Korea Combat Training Center to study the major factors that contribute to successfully completing military operations.

Keywords:

• Censored
• Penalized
• Quantile regression
• Selection bias
• Tree-structured model

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08 (Nonparametric regression)

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

Jaeoh Kim was supported by INHA UNIVERSITY Research Grant, and Sungwan Bang was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NO. 2020R1F1A1A01065107).