Regular score tests of independence in multivariate extreme values

• Type: Article in International Scientific Journal
• Date: 2005

Authors

Alexandra Ramos (Author) FEP; Anthony Ledford (Author) Other

Journal

Title: Extremes

Vol. 8 No. 1

Pages: 5-26

ISSN: 1386-1999

Publisher: Springer Nature

Indexing

ISI Web of Science

Scopus - 9 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-007-ESA

DOI: 10.1007/s10687-005-4857-4

Abstract (EN): The score tests of independence in multivariate extreme values derived by Tawn (Tawn, J.A., "Bivariate extreme value theory: models and estimation," Biometrika 75, 397-415, 1988) and Ledford and Tawn (Ledford, A.W. and Tawn, J.A., "Statistics for near independence in multivariate extreme values," Biometrika 83, 169-187, 1996) have non-regular properties that arise due to violations of the usual regularity conditions of maximum likelihood. Two distinct types of regularity violation are encountered in each of their likelihood frameworks: independence within the underlying model corresponding to a boundary point of the parameter space and the score function having an infinite second moment. For applications, the second form of regularity violation has the more important consequences, as it results in score statistics with non-standard normalisation and poor rates of convergence. The corresponding tests are difficult to use in practical situations because their asymptotic properties are unrepresentative of their behaviour for the sample sizes typical of applications, and extensive simulations may be needed in order to evaluate adequately their null distribution. Overcoming this difficulty is the primary focus of this paper. We propose a modification to the likelihood based approaches used by Tawn (Tawn, J.A., "Bivariate extreme value theory: models and estimation," Biometrika 75, 397-415, 1988) and Ledford and Tawn (Ledford, A.W. and Tawn, J.A., "Statistics for near independence in multivariate extreme values," Biometrika 83, 169-187, 1996) that provides asymptotically normal score tests of independence with regular normalisation and rapid convergence. The resulting tests are straightforward to implement and are beneficial in practical situations with realistic amounts of data. © 2005 Springer Science + Business Media, Inc.

Language: English

Type (Professor's evaluation): Scientific