A0536
Title: Smoothed kth power expectile regression with MQ-type function
Authors: Wenwu Gao - Anhui University (China) [presenting]
Abstract: Quantile regression, a powerful regression analysis method, estimates the conditional distribution of a response variable at different quantile levels. However, its non-differentiable loss function poses computational challenges. While asymmetric least squares regression simplifies the computation and asymmetric k-th power expectile regression offers higher asymptotic efficiency in certain cases, both methods suffer from non-differentiable loss functions. Convolution methods based on specific kernel functions have been employed to construct smooth approximations of the quantile regression loss. A novel and more intuitive approach for constructing smooth loss functions is proposed. Expressions for the smoothed versions of various loss functions are derived explicitly, including those for quantile regression $(k=1)$, expectile regression, and k-th power expectile regression $(1< k\leq 2)$. The transforms the original non-differentiable loss functions into infinitely differentiable ones, enabling faster gradient-based optimization techniques for solving quantile regression problems. Numerical simulations demonstrate that the proposed smooth loss functions maintain reliable accuracy while offering computational advantages. The contribution is not only the enrichment of the repertoire of non-smooth loss functions but also a provision of a new and efficient solution for regression analysis and related problems.
