Laws of large numbers for L -statistics

Rimas Norvaiša

International Journal of Stochastic Analysis, 1994, vol. 7, 1-19

Abstract:

Consider L n = n − 1 ∑ 1 ≤ i ≤ n c n i g ( X n : i ) for order statistics X n : i and let c n i = n ∫ ( i − 1 ) / n i / n J d λ for some (Lebesgue) λ -summable over ( 0 , 1 ) function J . Sufficient as well as necessary conditions for lim n L n = ∫ 0 1 J g d λ to hold almost surely and in probability are given. Superposition (or Nemytskii) operators have been used to derive the laws of large numbers for L -statistics from the laws of large numbers in quasi-Banach function spaces for the empirical distribution functions based on X 1 , … , X n .

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:574048

DOI: 10.1155/S1048953394000146

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