In many applications, subgroups with different parameters may exist even after accounting for the covariate effects, and it is important to identify the meaningful subgroups for better medical treatment or market segmentation. We propose a robust subgroup identification method based on median regression with concave fusion penalizations. The proposed method can simultaneously determine the number of subgroups, identify the group membership for each subject, and estimate the regression coefficients. Without requiring any parametric distributional assumptions, the proposed method is robust against outliers in the response and heteroscedasticity in the regression error. We develop a convenient algorithm based on local linear approximation, and establish the oracle property of the proposed penalized estimator and the model selection consistency for the modified Baycsian information criteria The numerical performance of the proposed method is assessed through simulation and the analysis of a heart disease data.
|Original language||English (US)|
|Number of pages||17|
|State||Published - 2019|
Bibliographical noteKAUST Repository Item: Exported on 2022-06-14
Acknowledged KAUST grant number(s): OSR-2015-CRG4-2582
Acknowledgements: The authors would like to thank the Editor, an associate editor, and two anonymous reviewers for their constructive comments that have significantly improved the paper. The research was partly supported by National Science Foundation grants DMS-1149355 and DMS-1712760, the OSR-2015-CRG4-2582 grant from KAUST, the National Natural Science Foundation of China grants 11671096, 11731011 and 11690013, and a fellowship from CSC (China Scholarship Council).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty