Nonparametric Expectile Regression Meets Deep Neural Networks: A Robust Nonlinear Variable Selection method

Abstract

ABSTRACT This paper investigates the variable selection problem in expectile regression under nonparametric conditions. In practical scenarios, data often exhibits heterogeneity and has a heavy‐tailed distribution. Expectile regression combines the advantages of mean regression and quantile regression, and can show the distribution characteristics of data at different expectile values. For actual data obtained, not all variables are important, selecting important variables can significantly reduce the cost of data collection and also reduce computational overhead. To extract representative feature subsets, various variable selection methods have been proposed for linear expectile regression models. However, in practice, there may be complex nonparametric relationships between explanatory and response variables. This paper extends the nonlinear variable selection method based on deep neural network DFS to nonparametric expectile regression to study the distribution correlation between explanatory and response variables in nonparametric situations. We validated the effectiveness and feasibility of the proposed method in numerical simulations and applied it to the used car transaction price dataset.