Weak convergence of empirical copula processes indexed by functions
نویسندگان
چکیده
DRAGAN RADULOVIĆ1, MARTEN WEGKAMP2 and YUE ZHAO3 1Department of Mathematics, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA. E-mail: [email protected] 2Department of Mathematics and Department of Statistical Science, Cornell University, 432 Malott Hall, Ithaca, NY 14853, USA. E-mail: [email protected] 3Department of Statistical Science, Cornell University, 310 Malott Hall, Ithaca, NY 14853, USA. E-mail: [email protected]
منابع مشابه
Weak Convergence of Stationary Empirical Processes
We offer an umbrella type result which extends the convergence of classical empirical process on the line to more general processes indexed by functions of bounded variation. This extension is not contingent on the type of dependence of the underlying sequence of random variables. As a consequence we establish the weak convergence for stationary empirical processes indexed by general classes of...
متن کاملAn elementary proof of the weak convergence of empirical processes
This paper develops a simple technique for proving the weak convergence of a stochastic process Z̄n(g) := ∫ g dZn, indexed by functions g in some class G. The main novelty is a decoupling argument that allows to derive asymptotic equicontinuity of the process {Z̄n(g), g ∈ G} from that of the basic process {Zn(t), t ∈ R}, with Zn(t) = Z̄n(ft) and ft(x) = 1(−∞,t](x). The method leads to novel result...
متن کاملEmpirical copula processes under serial dependence and weak smooth - ness conditions
The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2012) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random variables. In the first part of the talk, we extend his main result to the case of serial dependent random variables by means of the powerful and elegant fun...
متن کاملWeighted Sums and Residual Empirical Processes for Time-varying Processes
In the context of a time-varying AR-process we study both function indexed weighted sums, and sequential residual empirical processes. As for the latter it turns out that somewhat surprisingly, under appropriate assumptions, the non-parametric estimation of the parameter functions has a negligible asymptotic effect on the estimation of the error distribution. Function indexed weighted sum proce...
متن کاملAn Empirical Central Limit Theorem with applications to copulas under weak dependence
We state a multidimensional Functional Central Limit Theorem for weakly dependent random vectors. We apply this result to copulas. We get the weak convergence of the empirical copula process and of its smoothed version. The finite dimensional convergence of smoothed copula densities is also proved. A new definition and the theoretical analysis of conditional copulas and their empirical counterp...
متن کامل