Aaronson, J.; Burton, R.; Dehling, H.; Gilat, D.; Hill, T.; Weiss, B. Strong laws for \(L\)- and \(U\)-statistics. (English) Zbl 0863.60032 Trans. Am. Math. Soc. 348, No. 7, 2845-2866 (1996). Summary: Strong laws of large numbers are given for \(L\)-statistics (linear combinations of order statistics) and for \(U\)-statistics (averages of kernels of random samples) for ergodic stationary processes, extending classical theorems of Hoeffding and of Helmers for i.i.d. sequences. Examples are given to show that strong and even weak convergence may fail if the given sufficient conditions are not satisfied, and an application is given to estimation of correlation dimension of invariant measures. Cited in 1 ReviewCited in 31 Documents MSC: 60F15 Strong limit theorems 62G05 Nonparametric estimation 28D99 Measure-theoretic ergodic theory 62G30 Order statistics; empirical distribution functions Keywords:\(U\)-statistic; strong law of large numbers; ergodic stationary process PDFBibTeX XMLCite \textit{J. Aaronson} et al., Trans. Am. Math. Soc. 348, No. 7, 2845--2866 (1996; Zbl 0863.60032) Full Text: DOI