Robust rank-based variable selection in double generalized linear models with diverging number of parameters under adaptive Lasso

ABSTRACT

We propose a robust rank-based estimation and variable selection in double generalized linear models when the number of parameters diverges with the sample size. The consistency of the variable selection procedure and asymptotic properties of the resulting estimators are established under appropriate selection of tuning parameters. Simulations are performed to assess the finite sample performance of the proposed estimation and variable selection procedure. In the presence of gross outliers, the proposed method is showing that the variable selection method works better. For practical application, a real data application is provided using nutritional epidemiology data, in which we explore the relationship between plasma beta-carotene levels and personal characteristics (e.g. age, gender, fat, etc.) as well as dietary factors (e.g. smoking status, intake of cholesterol, etc.).

KEYWORDS:

• Double generalized linear models
• diverging number of parameters
• high leverage point
• rank-based
• variable selection

JEL classifications:

• 62G08
• 62J12
• 62K25

Acknowledgments

The authors are grateful to the associate editor and two anonymous referees for their constructive comments that substantially improved this paper. The first author gratefully acknowledges support from ONR (Office of Naval Research).

Disclosure statement

No potential conflict of interest was reported by the authors.