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] ; 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

     

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• 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.