Stochastic monotonicity of dependent variables given their sum

• Franco Pellerey ^[1] ; Jorge Navarro ^[2]
  1. [1] Polytechnic University of Turin

     Polytechnic University of Turin

     Torino, Italia

     
  2. [2] Universidad de Murcia

     Universidad de Murcia

     Murcia, España

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 31, Nº. 2, 2022, págs. 543-561
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Given a finite set of independent random variables, assume one can observe their sum, and denote with s its value. Efron in 1965, and Lehmann in 1966, described conditions on the involved variables such that each of them stochastically increases in the value s, i.e., such that the expected value of any non-decreasing function of the variable increases as s increases. In this paper, we investigate conditions such that this stochastic monotonicity property is satisfied when the assumption of independence is removed. Comparisons in the stronger likelihood ratio order are considered as well.