A contamination model for the stochastic order

P. C. Álvarez-Esteban (), E. del Barrio, J. A. Cuesta-Albertos and C. Matrán
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P. C. Álvarez-Esteban: Universidad de Valladolid
E. del Barrio: Universidad de Valladolid
J. A. Cuesta-Albertos: Universidad de Cantabria
C. Matrán: Universidad de Valladolid

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2016, vol. 25, issue 4, No 9, 774 pages

Abstract: Abstract 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.

Keywords: Stochastic order; Contamination model; Trimmed distribution; Uniformly consistent test; Asymptotics; Bootstrap; 60E15; 62G10; 62G35 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11749-016-0494-2

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