Interquantile shrinkage in additive models

ABSTRACT

In this paper, we investigate the commonality of nonparametric component functions among different quantile levels in additive regression models. We propose two fused adaptive group Least Absolute Shrinkage and Selection Operator penalties to shrink the difference of functions between neighbouring quantile levels. The proposed methodology is able to simultaneously estimate the nonparametric functions and identify the quantile regions where functions are unvarying, and thus is expected to perform better than standard additive quantile regression when there exists a region of quantile levels on which the functions are unvarying. Under some regularity conditions, the proposed penalised estimators can theoretically achieve the optimal rate of convergence and identify the true varying/unvarying regions consistently. Simulation studies and a real data application show that the proposed methods yield good numerical results.

Keywords:

• Additive models
• fused adaptive group LASSO
• interquantile shrinkage
• quantile regression

Acknowledgments

The authors sincerely thank the AE and two reviewers for their insightful comments that greatly improves the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Heng Lian is supported by City University of Hong Kong start up grant for new faculty (No. 7200521/MA).