A contamination model for the stochastic order

• P. C. Álvarez-Esteban ^[1] ; E. del Barrio ^[1] ; J. A. Cuesta-Albertos ^[2] ; C. Matrán ^[1]
  1. [1] Universidad de Valladolid

     Universidad de Valladolid

     Valladolid, España

     
  2. [2] Universidad de Cantabria

     Universidad de Cantabria

     Santander, España

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 25, Nº. 4, 2016, págs. 751-774
• Idioma: inglés
• DOI: 10.1007/s11749-016-0494-2
• Texto completo no disponible (Saber más ...)
• Resumen

  • Stochastic ordering among distributions has been considered in a variety of scenarios. However, it is often a restrictive model, not supported by the data even in cases in which the researcher tends to believe that a certain variable is somehow smaller than other. Alternatively, we propose to look at a more flexible version in which two distributions satisfy an approximate stochastic order relation if they are slightly contaminated versions of distributions for which stochastic order holds. The minimal level of contamination required for stochastic order to hold is used as a measure of deviation from exact stochastic order model. Our approach is based on the use of trimmings of probabilities. We discuss their connection to approximate stochastic order and provide theoretical support for its use in data analysis, proving uniform consistency and giving non-asymptotic bounds for the error probabilities of our tests. We provide simulation results and a case study for illustration.