Laws of large numbers for L-statistics. (1994)

• Record Type: Journal Article
• Authors: Norvaiša, Rimas
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 7:Number 2(1994)
• Page Start: 125
• Page End: 143
• Publication Date: 1994
• Subjects: order statistics -- law of large numbers -- L-statistics -- central limit theorem; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953394000146
• Languages: English
• ISSNs: 1048-9533

Abstract

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 .