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Abstract Linear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency between observation units, largely because such methods are not based upon a fully generative model of the data. For analysing spatially indexed data, we address this difficulty by generalizing the joint quantile regression model of Yang and Tokdar (Journal of the American Statistical Association, 2017, 112(519), 1107–1120) and characterizing spatial dependence via a Gaussian or t-copula process on the underlying quantile levels of the observation units. A Bayesian semiparametric approach is introduced to perform inference of model parameters and carry out spatial quantile smoothing. An effective model comparison criteria is provided, particularly for selecting between different model specifications of tail heaviness and tail dependence. Extensive simulation studies and two real applications to particulate matter concentration and wildfire risk are presented to illustrate substantial gains in inference quality, prediction accuracy and uncertainty quantification over existing alternatives.
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Robust estimation and inference for expected shortfall regression with many regressors
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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- PAR ID:
- 10514831
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Volume:
- 85
- Issue:
- 4
- ISSN:
- 1369-7412
- Format(s):
- Medium: X Size: p. 1223-1246
- Size(s):
- p. 1223-1246
- Sponsoring Org:
- National Science Foundation
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