A parametric alternative to the Hill estimator for heavy-tailed distributions |
| |
| Institution: | 1. Department of Applied Statistics, Yonsei University, South Korea;2. School of Economics, Yonsei University, South Korea;1. Finance Center Muenster, University of Muenster, Universitätsstr. 14-16, 48143 Münster, Germany;2. UBS AG, Group Risk Methodology, 8098 Zürich, Switzerland;1. Schools of Economics: Interdisciplinary Center, Tel-Aviv University and CEPR, Israel;2. Zicklin School of Business, Baruch College, United States;1. Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom;2. The Business School, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand |
| |
| Abstract: | Despite its wide use, the Hill estimator and its plot remain to be difficult to use in Extreme Value Theory (EVT) due to substantial sampling variations in extreme sample quantiles. In this paper, we propose a new plot we call the eigenvalue plot which can be seen as a generalization of the Hill plot. The theory behind the plot is based on a heavy-tailed parametric distribution class called the scaled Log phase-type (LogPH) distributions, a generalization of the ordinary LogPH distribution class which was previously used to model insurance claims data. We show that its tail property and moment condition are well aligned with EVT. Based on our findings, we construct the eigenvalue plot from fitting a shifted PH distribution to the excess log data with a minimal phase size. Through various numerical examples we illustrate and compare our method against the Hill plot. |
| |
| Keywords: | Hill estimator Tail index Extreme value theory Generalized Pareto distribution Scaled Log phase-type distribution |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
