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Laws of large numbers for L -statistics

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  • Rimas Norvaiša

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 .

Suggested Citation

  • Rimas Norvaiša, 1994. "Laws of large numbers for L -statistics," International Journal of Stochastic Analysis, Hindawi, vol. 7, pages 1-19, January.
    • Handle: RePEc:hin:jnijsa:574048
    DOI: 10.1155/S1048953394000146
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