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Abstract Expected shortfall (ES), also known as superquantile or conditional value-at-risk, is an important measure in risk analysis and stochastic optimisation and has applications beyond these fields. In finance, it refers to the conditional expected return of an asset given that the return is below some quantile of its distribution. In this paper, we consider a joint regression framework recently proposed to model the quantile and ES of a response variable simultaneously, given a set of covariates. The current state-of-the-art approach to this problem involves minimising a non-differentiable and non-convex joint loss function, which poses numerical challenges and limits its applicability to large-scale data. Motivated by the idea of using Neyman-orthogonal scores to reduce sensitivity to nuisance parameters, we propose a statistically robust and computationally efficient two-step procedure for fitting joint quantile and ES regression models that can handle highly skewed and heavy-tailed data. We establish explicit non-asymptotic bounds on estimation and Gaussian approximation errors that lay the foundation for statistical inference, even with increasing covariate dimensions. Finally, through numerical experiments and two data applications, we demonstrate that our approach well balances robustness, statistical, and numerical efficiencies for expected shortfall regression.
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A vignette on model-based quantile regression: analysing excess zero response
Quantile regression is widely seen as an ideal tool to understand complex predictor-response relations. Its biggest promise rests in its ability to quantify whether and how predictor effects vary across response quantile levels. But this promise has not been fully met due to a lack of statistical estimation methods that perform a rigorous, joint analysis of all quantile levels. This gap has been recently bridged by Yang and Tokdar [18]. Here we demonstrate how their joint quantile regression method, as encoded in the R package qrjoint, offers a comprehensive and model-based regression analysis framework. This chapter is an R vignette where we illustrate how to fit models, interpret coefficients, improve and compare models and obtain predictions under this framework. Our case study is an application to ecology where we analyse how the abundance of red maple trees depends on topographical and geographical features of the location. A complete absence of the species contributes excess zeros in the response data. We treat such excess zeros as left censoring in the spirit of a Tobit regression analysis. By utilising the generative nature of the joint quantile regression model, we not only adjust for censoring but also treat it as an object of independent scientific interest.
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- Award ID(s):
- 1613173
- PAR ID:
- 10309637
- Editor(s):
- Fan, Yanan; Nott, David; Smith, Michael S; Dortet-Bernadet, Jean-Luc.
- Date Published:
- Journal Name:
- Flexible Bayesian Regression Modelling
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1016/B978-0-12-815862-3.00008-1
