Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics
| Autor: | Olimjon Sh. Sharipov, Herold Dehling, Martin Wendler |
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| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Statistics and Probability
Numerical Analysis Degenerate energy levels Probability (math.PR) Block (permutation group theory) Hilbert space Mathematics - Statistics Theory Statistics Theory (math.ST) Space (mathematics) symbols.namesake Mixing (mathematics) Statistics symbols FOS: Mathematics von Mises yield criterion Statistics Probability and Uncertainty Random variable Mathematics - Probability Central limit theorem Mathematics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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