On quadratic forms in multivariate generalized hyperbolic random vectors

• 成果类型: Article
• 署名作者: Broda, Simon A.; Zambrano, Juan Arismendi
• 署名单位: Maynooth University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa067
• 发表日期: 2021
• 页码: 413424
• 关键词: small sample properties; expected shortfall; saddlepoint approximation; mendelian randomization; weak instruments; time-series; distributions; estimator; variables; portfolio

摘要

This article presents exact and approximate expressions for tail probabilities and partial moments of quadratic forms in multivariate generalized hyperbolic random vectors. The derivations involve a generalization of the classic inversion formula for distribution functions (Gil-Pelaez, 1951). Two numerical applications are considered: the distribution of the two-stage least squares estimator and the expected shortfall of a quadratic portfolio.