| 概要 |
The expected shortfall (ES) regression is a useful tool to analyze the relation between the response variable and the covariates through quantile and conditional mean. 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. In this paper, to tackle both non-linearity and high-dimensionality, we assume additive models for both quantile and expected shortfall in the high-dimensional settings and consider the group Lasso and SCAD estimators. We establish the oracle inequality and the oracle property for them. Our theoretical results imply that quantile estimation does not affect ES estimation asymptotically. We present numerical results that demonstrate satisfactory performances in model selection, estimation accuracy, and prediction error for a moderate sample size. This is joint work with Po-Hsiang Peng. |
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