A1032
Title: Weak convergence of the function-indexed sequential empirical process for nonstationary time series
Authors: Florian Scholze - RWTH Aachen University/ University of Bamberg (Germany) [presenting]
Abstract: Sequential empirical processes have several statistical applications, including change detection and goodness-of-fit testing. Studying their behavior in different settings is, therefore, of both theoretical and practical interest. So far, the literature on the weak convergence of the function-indexed sequential empirical process under dependence seems to be limited to the stationary case. To partially close this gap, its weak convergence is studied in a nonstationary setting, and it is shown to be asymptotically equicontinuous, provided suitable maximal inequalities are available for the increments of its nonsequential counterpart. The assumed maximal inequalities implicitly contain some nonspecific dependence restrictions, but no additional dependence restrictions are imposed. Thereby, a certain level of generality is achieved, which enables a range of possible applications. Limitations, possible extensions and statistical applications are discussed.
