A class of bootstrap tests on the tail index
- Authors
- Hwang, Eunju
- Issue Date
- May-2023
- Publisher
- TAYLOR & FRANCIS INC
- Keywords
- 62G10; 62G30; Bootstrap test; Empirical distribution function; Primary: 62F40; Secondary: 62G32; Subsampling; Tail index
- Citation
- COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, v.52, no.5, pp.1786 - 1804
- Journal Title
- COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
- Volume
- 52
- Number
- 5
- Start Page
- 1786
- End Page
- 1804
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/87775
- DOI
- 10.1080/03610918.2021.1890772
- ISSN
- 0361-0918
- Abstract
- This work proposes powerful tests using bootstrap methods for the tail index in the family of distribution functions with nondegenerate right tail. It is of interest to test whether the right tail of a distribution function is the same as or heavier than that of the Pareto distribution with index m 0 for some m 0, vs. alternatively the right tail is lighter. Based on the nonparametric tests of Jureckova and Picek (2001, A class of tests on the tail index, Extreme 4:2, 165–183) that use empirical distribution functions of sample maxima, the proposed bootstrap tests employ two-stage subsamplings: One is subsampling from the sample maxima to be applicable even to the heavy tailed index and the other is subsampling from collections of empirical distributions of the sample maxima. We show the first-order validity of the bootstrap for the nonparametric test and construct bootstrap test statistics. The limiting distribution of the bootstrap test statistics in the null hypothesis is established and the consistency of the bootstrap tests is verified. Applications of the proposed bootstrap tests are given to autoregressive time series models. A simulation study is conducted to see performance of the bootstrap tests and it illustrates that the proposed bootstrap tests outperform the existing ones. Real data of heavy tailed financial stock indices are applied to the proposed bootstrap tests. © 2021 Taylor & Francis Group, LLC.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - 사회과학대학 > 응용통계학과 > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.