Sparse reduced-rank regression for multivariate varying-coefficient models

ABSTRACT

Varying-coefficient regression is a popular statistical tool that models the way a certain variable modulates the effect of other predictors nonlinearly. However, a majority of the VC regression models consider univariate responses; the case of multivariate responses have received relatively lesser attention. In this paper, we propose a robust multivariate varying-coefficient model based on rank loss that models the relationships among different responses via reduced-rank regression and penalized variable selection. Some asymptotic results are also established for the proposed methods. Using synthetic data, we investigate the finite sample performance and robustness properties of the estimator. We also illustrate our methodology by application to a real dataset on periodontal disease.

Keywords:

• Rank regression
• variable selection
• varying-coefficient models

Acknowledgments

The authors sincerely thank the editors and the anonymous reviewer for their detailed review of the work which has greatly improved our manuscript. The work of Zhang is partially supported by the Fundamental Research Funds for the Central Universities (No. JBK2001001, JBK1806002 and JBK140507) of China. Rui Li's research was supported by National Social Science fund of China [No. 17BTJ025]. Bandyopadhyay acknowledges funding support of grants R01DE024984 and P30CA016059, awarded by the United States National Institutes of Health.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of Zhang is partially supported by the Fundamental Research Funds for the Central Universities [grant numbers JBK2001001, JBK1806002 and JBK140507] of China. Rui Li's research was supported by the National Social Science fund of China [grant number 17BTJ025]. Bandyopadhyay acknowledges funding support of grants R01DE024984 and P30CA016059, awarded by the United States National Institutes of Health.