This talk is concerned with noncentral limit theorems (NCLT) for statistical functionals based on strictly stationary time series exhibiting long-range dependence. The key tool is an NCLT for empirical processes of long-memory data with respect to nonuniform sup-norms. Using a modified Functional Delta Method, based on the new concept of quasi-Hadamard differentiability, one can easily derive the asymptotic distribution of fairly general statistics, including L-statistics as well as nondegenerate and degenerate U- and V-statistics with unbounded kernel.
Beutner, E. and Zähle, H. (2010). A modified functional delta method and its application to the estimation of risk functionals. Journal of Multivariate Analysis, 101, 2452-2463.
Beutner, E., and Zähle, H. (2011). Deriving the asymptotic distribution of U- and V-statistics using weighted empirical processes.
Beutner, E., Wu, W.B. and Zähle, H. (2011). Noncentral limit theorems for statistical functionals based on long-memory sequences.
Keywords: Long-range dependence; Noncentral limit theorem; Weighted empirical process; Quasi-Hadamard differentiability
Biography: Henryk Zähle is Professor of Stochastics at Saarland University, Saarbrücken, Germany. He received the PhD degree in Mathematics from the Technical University Berlin in 2004. His research interests include asymptotic properties of nonparametric estimators, as central and non-central limit theorems, Marcinkiewicz–Zygmund laws of large numbers and qualitative robustness.