A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular ℤd-actions. (28th March 2018)

• Record Type: Journal Article
• Authors: Bhattacharya, Ayan; Roy, Parthanil
• Is Part Of: Journal of applied probability. Volume 55:Number 1(2018)
• Page Start: 179
• Page End: 195
• Publication Date: 2018-03-28
• Subjects: Long range dependence, -- stationary SαS random field, -- nonsingular group action, -- extreme value theory, -- statistical hypothesis testing; Primary 60G10, -- 60G60, -- 62H15, -- Secondary 37A40; 519.2
• DOI: 10.1017/jpr.2018.12
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: Based on the ratio of two block maxima, we propose a large sample test for the length of memory of a stationary symmetric α-stable discrete parameter random field. We show that the power function converges to 1 as the sample-size increases to ∞ under various classes of alternatives having longer memory in the sense of Samorodnitsky (2004). Ergodic theory of nonsingular ℤ d -actions plays a very important role in the design and analysis of our large sample test.