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Variance-reduced risk inference in semi-supervised settings

Einmahl,John
; 
Peng,Liang
Abstract
In the estimating equation framework, this paper develops a variance-reduced estimation procedure when, next to a short primary sample of interest, another longer auxiliary sample is available. The proposed method does not require modeling and inferring the dependence between the primary and auxiliary samples. We apply the proposed method to develop a novel variance-reduced estimator for three popular risk measures: Value-at-Risk, Expected Shortfall, and Expectile. A simulation study confirms the good performance of our method. Finally, an application to hurricane losses is presented.
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2025-11
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Tilburg University Research Output Collection
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einmahl_saj.pdf
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Keywords
estimating equation, risk measure, semi-supervised inference, variance reduction
Citation
Einmahl, J & Peng, L 2025, 'Variance-reduced risk inference in semi-supervised settings', Scandinavian Actuarial Journal. https://doi.org/10.1080/03461238.2025.2587657
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https://hdl.handle.net/20.500.14602/104401
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