An Empirical Process Central Limit Theorem for Multidimensional Dependent Data

Details An Empirical Process Central Limit Theorem for Multidimensional Dependent Data An Empirical Process Central Limit Theorem for Multidimensional Dependent Data

2011-10-05

arxiv.org/abs/1110.0963v1

Mathematics

Probability

Scientific paper

Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$, under which weak convergence of $(U_n(t))_{t\in\R^d}$ can be proved. This is particularly useful when dealing with data arising from dynamical systems or functional of Markov chains. This result improves those of [DDV09] and [DD11], where the technique was first introduced, and provides new applications.

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