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On the concept of B-statistical uniform integrability of weighted sums of random variables and the law of large numbers with mean convergence in the statistical sense

  • Manuel Ordóñez Cabrera [1] Árbol académico ; Andrew Rosalsky [2] ; Mehmet Ünver [3] ; Andrei Volodin [4]
    1. [1] Universidad de Sevilla

      Universidad de Sevilla

      Sevilla, España

    2. [2] University of Florida

      University of Florida

      Estados Unidos

    3. [3] Ankara University

      Ankara University

      Turquía

    4. [4] University of Regina

      University of Regina

      Canadá

  • Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 30, Nº. 1, 2021, págs. 83-102
  • Idioma: inglés
  • DOI: 10.1007/s11749-020-00706-2
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • In this correspondence, for a nonnegative regular summability matrix B and an array {ank} of real numbers, the concept of B-statistical uniform integrability of a sequence of random variables {Xk} with respect to {ank} is introduced. This concept is more general and weaker than the concept of {Xk} being uniformly integrable with respect to {ank}. Two characterizations of B-statistical uniform integrability with respect to {ank} are established, one of which is a de La Vallée Poussin-type characterization. For a sequence of pairwise independent random variables {Xk} which is B-statistically uniformly integrable with respect to {ank}, a law of large numbers with mean convergence in the statistical sense is presented for ∑∞k=1ank(Xk−EXk) as n→∞. A version is obtained without the pairwise independence assumption by strengthening other conditions.


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