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Strong Laws for L- and U-Statistics
Transactions of the American Mathematical Society
  • J. Aaronson, Tel Aviv University
  • R. Burton, Oregon State University
  • H. Dehling, Tel Aviv University
  • D. Gilat, Tel Aviv University
  • Theodore P. Hill, Georgia Institute of Technology - Main Campus
  • B. Weiss, Hebrew University of Jerusalem
Publication Date

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 iid 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.

Citation Information
J. Aaronson, R. Burton, H. Dehling, D. Gilat, et al.. "Strong Laws for L- and U-Statistics" Transactions of the American Mathematical Society Vol. 348 Iss. 7 (1996) p. 2845 - 2866
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