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

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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.