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A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular ℤd-actions

Part of: Multivariate analysis Ergodic theory Stochastic processes

Published online by Cambridge University Press:  28 March 2018

Ayan Bhattacharya  and
Parthanil Roy
Ayan Bhattacharya*
Affiliation:
CWI, Amsterdam
Parthanil Roy*
Affiliation:
ISI, Bangalore
*
* Postal address: Stochastics group, CWI, Amsterdam, North Holland, 1098XG, Netherlands. Email address: [email protected]
** Postal address: Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, RVCE Post, Bangalore, 560059, India.
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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 ℤd-actions plays a very important role in the design and analysis of our large sample test.

Keywords

Long range dependencestationary SαS random fieldnonsingular group actionextreme value theorystatistical hypothesis testing

MSC classification

Primary: 60G10: Stationary processes 60G60: Random fields 62H15: Hypothesis testing
Secondary: 37A40: Nonsingular (and infinite-measure preserving) transformations
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 179 - 195
Copyright
Copyright © Applied Probability Trust 2018 

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