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The empirical process of some
long-range dependent sequences
Murad S. Taqqu
Let be a stationary, mean-zero Gaussian process with
satisfying and where D is small and L is slowly varying at infinity.
Consider the two-parameter empirical process for
where G is any measurable function. Non-central limit theorems are
obtained for and they are used to derive the asymptotic behavior of some suitably normalized von Mises statistics
and U-statistics based on the 's.
The limiting processes are structurally different
from those encountered in the i.i.d. case.