Functional central limit theorem and Marcinkiewicz strong law of large numbers for Hilbert-valued U-statistics of absolutely regular data
Author:
Affiliation:
1. Institut de Recherche Mathématique Avancée UMR 7501, Université de Strasbourg and CNRS 7 rue René Descartes 67000 Strasbourg, France
Publisher
Institute of Mathematical Statistics
Reference32 articles.
1. Rio, E. (2000). Théorie Asymptotique des Processus Aléatoires Faiblement Dépendants. Mathématiques & Applications (Berlin) [Mathematics & Applications] 31. Berlin: Springer.
2. Halmos, P. R. (1946). The theory of unbiased estimation. The Annals of Mathematical Statistics 17, 34–43.
3. Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution. The Annals of Mathematical Statistics 19, 293–325.
4. Aaronson, J., Burton, R., Dehling, H., Gilat, D., Hill, T. and Weiss, B. (1996). Strong laws for L- and U-statistics. Transactions of the American Mathematical Society 348, 2845–2866.
5. Arcones, M. A. (1998). The law of large numbers for U-statistics under absolute regularity. Electronic Communications in Probability 3, 13–19.
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