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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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Homogeneity Structure Learning in Large-scale Panel Data with Heavy-tailed Errors
Large-scale panel data is ubiquitous in many modern data science applications. Conventional panel data analysis methods fail to address the new challenges, like individual impacts of covariates, endogeneity, embedded low-dimensional structure, and heavy-tailed errors, arising from the innovation of data collection platforms on which applications operate. In response to these challenges, this paper studies large-scale panel data with an interactive effects model. This model takes into account the individual impacts of covariates on each spatial node and removes the exogenous condition by allowing latent factors to affect both covariates and errors. Besides, we waive the sub-Gaussian assumption and allow the errors to be heavy-tailed. Further, we propose a data-driven procedure to learn a parsimonious yet flexible homogeneity structure embedded in high-dimensional individual impacts of covariates. The homogeneity structure assumes that there exists a partition of regression coeffcients where the coeffcients are the same within each group but different between the groups. The homogeneity structure is flexible as it contains many widely assumed low dimensional structures (sparsity, global impact, etc.) as its special cases. Non-asymptotic properties are established to justify the proposed learning procedure. Extensive numerical experiments demonstrate the advantage of the proposed learning procedure over conventional methods especially when the data are generated from heavy-tailed distributions.
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- PAR ID:
- 10217339
- Date Published:
- Journal Name:
- Journal of machine learning research
- Volume:
- 22
- ISSN:
- 1533-7928
- Page Range / eLocation ID:
- 1-42
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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