Weak convergence of the weighted sequential empirical process of some long-range dependent data
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Date
2014-09-05
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Abstract
Let (X_k)k>=1 be a Gaussian long-range dependent process with EX_1 = 0, EX^2_1
1 = 1
and covariance function r(k) = k^(-D)L(k). For any measurable function G let
(Y_k)k>= 1 = (G(X_k))k>= 1. We study the asymptotic behaviour of the associated sequential
empirical process (R_N(x,t)) with respect to a weighted sup-norm ||*||w.
We show that, after an appropriate normalization, (R_N(x,t)) converges weakly in
the space of c adl ag functions with nite weighted norm to a Hermite process.
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Keywords
sequential empirical process, modified functional delta method, weighted norm, long-range dependence