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- Title
A Nonparametric Test for Weak Dependence Against Strong Cycles and its Bootstrap Analogue.
- Authors
Hidalgo, Javier
- Abstract
We examine a test for the hypothesis of weak dependence against strong cyclical components. We show that the limiting distribution of the test is a Gumbel distribution, denoted G(·). However, since G(·) may be a poor approximation to the finite sample distribution, being the rate of the convergence logarithmic [see Hall Journal of Applied Probability (1979) , Vol. 16, pp. 433–439], inferences based on G(·) may not be very reliable for moderate sample sizes. On the other hand, in a related context, Hall [Probability Theory and Related Fields (1991) , Vol. 89, pp. 447–455] showed that the level of accuracy of the bootstrap is significantly better. For that reason, we describe an approach to bootstrapping the test based on Efron's [Annals of Statistics (1979) , Vol. 7, pp. 1–26] resampling scheme of the data. We show that the bootstrap principle is consistent under very mild regularity conditions.
- Subjects
DISTRIBUTION (Probability theory); STATISTICAL bootstrapping; STATISTICAL sampling; MATHEMATICAL analysis; RESAMPLING (Statistics)
- Publication
Journal of Time Series Analysis, 2007, Vol 28, Issue 3, p307
- ISSN
0143-9782
- Publication type
Article
- DOI
10.1111/j.1467-9892.2006.00510.x