Weak convergence of the weighted sequential empirical process of some long-range dependent data

作者：Buchsteiner Jannis^*

来源：Statistics & Probability Letters, 2015, 96: 170-179.

DOI：10.1016/j.spl.2014.09.022

• Sequential empirical process
• Long-range dependence
• Weighted norm
• Modified functional delta method

Let (X-k)(k >= 1) be a Gaussian long-range dependent process with EX1 = 0, EX12 = 1 and covariance function r(k) = k L-D(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 parallel to.parallel to(w) . We show that, after an appropriate normalization, (R-N(x, t)) converges weakly in the space of cadlag functions with finite weighted norm to a Hermite process.

• 出版日期2015-1