Modelling additive extremile regression by iteratively penalized least asymmetric weighted squares and gradient descent boosting

Abstract

Quantile regression has emerged as one of the standard tools for regression analysis that enables a proper assessment of the complete conditional distribution of responses. This article considers a valuable alternative class to quantiles, called extremiles. Extremiles bear much better than quantiles the burden of representing an alert risk measure to the magnitude of infrequent catastrophic losses. Additive regression model has concentrated on making the regression structure more flexible by including nonlinear effects of continuous covariates and interaction effects. As a consequence, additive extremile regression based on minimizing an asymmetrically weighted sum of squared residuals is introduced. Different estimation procedures are presented including iteratively penalized least asymmetric weighted squares and gradient descent boosting. The properties of these procedures are investigated in a simulation study and an analysis of tropical cyclone intensity of the North Atlantic which reveals the function of variable selection by modelling additive extremile regression simultaneously.

KEYWORDS:

• Extremile regression
• additive model
• iteratively penalized least asymmetric weighted squares
• gradient descent boosting
• tropical cyclone intensity of North Atlantic

Acknowledgments

The author wishes to thank editor and anonymous reviewer for their helpful suggestions which led to an improvement of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Availability of supporting data

The data set analysed during the current study is available from the corresponding author on reasonable request.

Additional information

Funding

I also acknowledge the fundings from the National Social Science Fund of China [grant number 22ATJ005] and Major Project of the MOE (China) National Key Research Bases for Humanities and Social Sciences [22JJD910003].