A0427
Title: Expected shortfall regression for high-dimensional additive models
Authors: Toshio Honda - Hitotsubashi University (Japan) [presenting]
PoHsiang Peng - National Tsing Hua University (Taiwan)
Abstract: The expected shortfall (ES) regression is a useful tool to analyze the relation between the response variable and the covariates through quantile and conditional means. As is well-known, there is no single loss function for expected shortfall estimation. Recently, a two-step procedure for ES regression was proposed, and this is successful due to the Neyman orthogonality. Then, based on the findings, high dimensional linear ES regression models and nonparametric ES models were considered. To tackle both non-linearity and high-dimensionality, additive models are assumed for both quantile and expected shortfall in the high-dimensional settings, and the group Lasso and SCAD estimators are considered. The oracle inequality and the oracle property are established for them. Theoretical results imply that quantile estimation does not affect ES estimation asymptotically. Numerical results are presented that demonstrate satisfactory performances in model selection, estimation accuracy, and prediction error for a moderate sample size.
