Rimas Norvaiša, "Laws of large numbers for -statistics", International Journal of Stochastic Analysis, vol. 7, Article ID 574048, 19 pages, 1994. https://doi.org/10.1155/S1048953394000146
Laws of large numbers for -statistics
Consider for order statistics and let for some (Lebesgue) -summable over function . Sufficient as well as necessary conditions for to hold almost surely and in probability are given. Superposition (or Nemytskii) operators have been used to derive the laws of large numbers for -statistics from the laws of large numbers in quasi-Banach function spaces for the empirical distribution functions based on .
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