Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics

JOURNAL OF MULTIVARIATE ANALYSIS

卷:133

Article

Dehling, Herold¹  Sharipov, Olimjon Sh.²  Wendler, Martin¹ 

[1] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany

[2] Natl Univ Uzbekistan, Inst Math, Tashkent 100125, Uzbekistan

关键词: Absolute regularity;    Near epoch dependence;    Hilbert space;    Block bootstrap;    Functional time series;   

DOI  :  10.1016/j.jmva.2014.09.011

来源: Elsevier

【 摘 要 】

Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly dependent in the sense of near epoch dependence, where the underlying process fulfills some mixing conditions. As parametric inference in an infinite dimensional space is difficult, we show that the nonoverlapping block bootstrap is consistent. Furthermore, we show how these results can be used for degenerate von Mises-statistics. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free