Gardado en:
| Main Authors: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Subjects: | |
| Acceso en liña: | https://arxiv.org/abs/2302.04539 |
| Tags: |
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Table of Contents:
- In this note, we investigate the convergence of a $U$-statistic of order two having stationary ergodic data. We will find sufficient conditions for the almost sure and $L^1$ convergence and present some counter-examples showing that the $U$-statistic itself might fail to converge: centering is needed as well as boundedness of $\sup_{j\geq 2}\mathbb{E}[|h(X_1,X_j)|]$.