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M. Wendler

Publications and source records attributed to M. Wendler.

2 recordsLinked to original sources
arXiv2014

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

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.

math.ST↗
arXiv2012

Normal Limits, Nonnormal Limits, and the Bootstrap for Quantiles of Dependent Data

We will show under very weak conditions on differentiability and dependence that the central limit theorem for quantiles holds and that the block bootstrap is weakly consistent. Under slightly stronger conditions, the bootstrap is strongly consistent. Without the differentiability condition, quantiles might have a non-normal asymptotic distribution and the bootstrap might fail.

math.ST↗