A1776
Title: Estimation and inference for nonparametric expected shortfall regression over RKHS
Authors: Yue Wang - University of Science and Technology Of China (China) [presenting]
Abstract: Expected shortfall (ES) has emerged as an important metric for characterizing the tail behavior of a random outcome, specifically associated with rarer events that entail severe consequences. In climate science, the threats of flooding and heatwaves loom large, impacting natural environments and human communities. In actuarial studies, a key observation in modeling insurance claim sizes is that features exhibit distinct effects in explaining small and large claims. Nonparametric expected shortfall regression constitutes a class of statistical methods for tail learning. These methods directly target upper and lower tail averages and empower practitioners to address complex questions that are beyond the reach of mean regression-based approaches. Using kernel ridge regression, a two-step nonparametric ES estimator is introduced that involves a plugged-in quantile function estimate without sample-splitting. Non-asymptotic estimation and Gaussian approximation error bounds are provided, depending explicitly on the effective dimension, sample size, regularization parameters, and quantile estimation error. To construct pointwise confidence bands, a fast multiplier bootstrap procedure is proposed and its validity is established. The finite-sample performance of the proposed method is demonstrated.
