Asymptotic distribution of two-sample empirical U-quantiles with applications to robust tests for structural change
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Date
2010-10-27
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Abstract
We derive the asymptotical distributions of two-sample U-statistics and
two-sample empirical U-quantiles in the case of weakly dependent data. Our
results apply to observations that can be represented as functionals of absolutely
regular processes, including e.g. many classical time series models as
well as data from chaotic dynamical systems. Based on these theoretical results
we propose a new robust nonparametric test for the two-sample location
problem, which is constructed from the median of pairwise differences between
the two samples. We inspect the properties of the test in the case of
weakly dependent data and compare the performance with classical tests such
as the t-test and Wilcoxon’s two-sample rank test with corrections for dependencies.
Simulations indicate that the new test offers better power even than
the Wilcoxon test in case of skewed and heavy tailed distributions, if at least
one of the two samples is not very large. The test is then applied for detecting
shifts of location in some weakly dependent time series, which are contaminated
by outliers.
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Keywords
Functional of an absolutely regular process, Hodges-Lehmann estimator, Two-sample location problem, U-statistic, Weak dependence