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UBC Theses and Dissertations

Risk region estimation for light-tailed multivariate samples Hou, Yiwei


Estimation of multivariate quantile regions with very small probabilities, referred to as risk regions in this report, plays an important part in various applications. Yet, it is a difficult problem since such regions contain hardly any or no data. Existing methods address the problem only for heavy-tailed distributions or for bivariate distributions with non-degenerate exponent measure that do not include the cases of asymptotic independence. In this report, we propose a more flexible framework to supplement existing approaches to risk region estimation by allowing tails of the underlying distribution to be light as well as covering situations of tail independence. In particular, we concentrate on a class of distributions assumed to have a density function with homothetic level sets. In simulation studies, reasonable performance of our proposed method is demonstrated. We also present two real-life applications to further illustrate the flexibility and performance of our method.

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