IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v25y2016i4d10.1007_s11749-016-0494-2.html
   My bibliography  Save this article

A contamination model for the stochastic order

Author

Listed:
  • 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)

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.

Suggested Citation

  • P. C. Álvarez-Esteban & E. del Barrio & J. A. Cuesta-Albertos & C. Matrán, 2016. "A contamination model for the stochastic order," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 751-774, December.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:4:d:10.1007_s11749-016-0494-2
    DOI: 10.1007/s11749-016-0494-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-016-0494-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-016-0494-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Russell Davidson & Jean-Yves Duclos, 2013. "Testing for Restricted Stochastic Dominance," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 84-125, January.
    2. Linton, Oliver & Song, Kyungchul & Whang, Yoon-Jae, 2010. "An improved bootstrap test of stochastic dominance," Journal of Econometrics, Elsevier, vol. 154(2), pages 186-202, February.
    3. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    4. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 735-765.
    5. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    6. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
    7. Alvarez-Esteban, Pedro Cesar & del Barrio, Eustasio & Cuesta-Albertos, Juan Antonio & Matran, Carlos, 2008. "Trimmed Comparison of Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 697-704, June.
    8. Arcones M. A. & Kvam P. H. & Samaniego F. J., 2002. "Nonparametric Estimation of a Distribution Subject to a Stochastic Precedence Constraint," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 170-182, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Montes, Ignacio & Salamanca, Juan Jesús & Montes, Susana, 2020. "A modified version of stochastic dominance involving dependence," Statistics & Probability Letters, Elsevier, vol. 165(C).
    2. Gordon Anderson & Maria Grazia Pittau & Roberto Zelli & Jasmin Thomas, 2018. "Income Inequality, Cohesiveness and Commonality in the Euro Area: A Semi-Parametric Boundary-Free Analysis," Econometrics, MDPI, vol. 6(2), pages 1-20, March.
    3. Eustasio del Barrio & Hristo Inouzhe & Carlos Matrán, 2020. "Box-Constrained Monotone Approximations to Lipschitz Regularizations, with Applications to Robust Testing," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 65-87, October.
    4. E. Barrio & H. Inouzhe & C. Matrán, 2020. "On approximate validation of models: a Kolmogorov–Smirnov-based approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 938-965, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Khaled, Mohamad A. & Makdissi, Paul & Yazbeck, Myra, 2018. "Income-related health transfers principles and orderings of joint distributions of income and health," Journal of Health Economics, Elsevier, vol. 57(C), pages 315-331.
    2. David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2020. "Bayesian assessment of Lorenz and stochastic dominance," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(2), pages 767-799, May.
    3. David Lander & David Gunawan & William E. Griffiths & Duangkamon Chotikapanich, 2016. "Bayesian Assessment of Lorenz and Stochastic Dominance Using a Mixture of Gamma Densities," Department of Economics - Working Papers Series 2023, The University of Melbourne.
    4. Wen-Hao Chen & Jean-Yves Duclos, 2011. "Testing for poverty dominance: an application to Canada," Canadian Journal of Economics, Canadian Economics Association, vol. 44(3), pages 781-803, August.
    5. Lee, Kyungho & Linton, Oliver & Whang, Yoon-Jae, 2023. "Testing for time stochastic dominance," Journal of Econometrics, Elsevier, vol. 235(2), pages 352-371.
    6. Donald, Stephen G. & Hsu, Yu-Chin, 2014. "Estimation and inference for distribution functions and quantile functions in treatment effect models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 383-397.
    7. Stengos, Thanasis & Thompson, Brennan S., 2012. "Testing for bivariate stochastic dominance using inequality restrictions," Economics Letters, Elsevier, vol. 115(1), pages 60-62.
    8. Sokbae Lee & Yoon-Jae Whang, 2009. "Nonparametric Tests of Conditional Treatment Effects," Cowles Foundation Discussion Papers 1740, Cowles Foundation for Research in Economics, Yale University.
    9. Al-Khazali, Osamah & Mirzaei, Ali, 2017. "Stock market anomalies, market efficiency and the adaptive market hypothesis: Evidence from Islamic stock indices," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 51(C), pages 190-208.
    10. Gonzalo, Jesús & Olmo, José, 2008. "Testing downside risk efficiency under market distress," UC3M Working papers. Economics we084321, Universidad Carlos III de Madrid. Departamento de Economía.
    11. Miguel A. Delgado & Juan Carlos Escanciano, 2013. "Conditional Stochastic Dominance Testing," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 16-28, January.
    12. Stelios Arvanitis & Thierry Post & Nikolas Topaloglou, 2021. "Stochastic Bounds for Reference Sets in Portfolio Analysis," Management Science, INFORMS, vol. 67(12), pages 7737-7754, December.
    13. Hongyi Jiang & Zhenting Sun & Shiyun Hu, 2023. "A Nonparametric Test of $m$th-degree Inverse Stochastic Dominance," Papers 2306.12271, arXiv.org, revised Jul 2023.
    14. Jesus Gonzalo & Jose Olmo, 2014. "Conditional Stochastic Dominance Tests In Dynamic Settings," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(3), pages 819-838, August.
    15. Ng, Pin & Wong, Wing-Keung & Xiao, Zhijie, 2017. "Stochastic dominance via quantile regression with applications to investigate arbitrage opportunity and market efficiency," European Journal of Operational Research, Elsevier, vol. 261(2), pages 666-678.
    16. Ai, Chunrong & Linton, Oliver & Zhang, Zheng, 2022. "Estimation and inference for the counterfactual distribution and quantile functions in continuous treatment models," Journal of Econometrics, Elsevier, vol. 228(1), pages 39-61.
    17. Rahul Deb & Ludovic Renou, 2022. "Which wage distributions are consistent with statistical discrimination?," Working Papers tecipa-736, University of Toronto, Department of Economics.
    18. Lean, Hooi-Hooi & Wong, Wing-Keung & Zhang, Xibin, 2008. "The sizes and powers of some stochastic dominance tests: A Monte Carlo study for correlated and heteroskedastic distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(1), pages 30-48.
    19. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    20. Brendan K. Beare & Jackson D. Clarke, 2022. "Modified Wilcoxon-Mann-Whitney tests of stochastic dominance," Papers 2210.08892, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:25:y:2016:i:4:d:10.1007_s11749-016-0494-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.