IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v21y2012i4p730-756.html
   My bibliography  Save this article

Nonparametric tests for stochastic ordering

Author

Listed:
  • Teresa Ledwina
  • Grzegorz Wyłupek

Abstract

We present two new tests for stochastic ordering in a standard two-sample scheme. We approach the problem via its reparametrization in terms of Fourier coefficients in some corresponding system of functions and combining the resulting empirical Fourier coefficients. The empirical Fourier coefficients can be seen to be the asymptotically optimal linear rank statistics for the local sequences of nonparametric alternatives related to the introduced system of functions. Therefore, our first construction of the test is via multiple testing. The second test is based on sum of squares of censored empirical Fourier coefficients with the number of summands determined via a new model selection rule. The selection rule is fully automatic. Extensive simulations show that the new solutions improve upon existing tests based on adjusted variants of classical Kolmogorov–Smirnov, Anderson–Darling and L 1 -distance-based statistics, among others. We show that both tests control the error of the first kind for any fixed sample sizes and are capable of detecting essentially any alternative as the sample sizes are growing to infinity. We also discuss several aspects of our constructions, including possible efficiency calculations and asymptotic comparisons. Copyright Sociedad de Estadística e Investigación Operativa 2012

Suggested Citation

  • Teresa Ledwina & Grzegorz Wyłupek, 2012. "Nonparametric tests for stochastic ordering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 730-756, December.
  • Handle: RePEc:spr:testjl:v:21:y:2012:i:4:p:730-756
    DOI: 10.1007/s11749-011-0278-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11749-011-0278-7
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s11749-011-0278-7?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. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    2. R. L. Eubank, 2000. "Testing for No Effect by Cosine Series Methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 747-763, December.
    3. Russell Davidson & Jean-Yves Duclos, 2013. "Testing for Restricted Stochastic Dominance," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 84-125, January.
    4. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    5. Escanciano, Juan Carlos & Mayoral, Silvia, 2010. "Data-driven smooth tests for the martingale difference hypothesis," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1983-1998, August.
    6. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
    7. Christensen, Ronald & Sun, Siu Kei, 2010. "Alternative Goodness-of-Fit Tests for Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 291-301.
    8. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
    9. Hall, Peter & Yatchew, Adonis, 2005. "Unified approach to testing functional hypotheses in semiparametric contexts," Journal of Econometrics, Elsevier, vol. 127(2), pages 225-252, August.
    10. 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.
    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. Ledwina, Teresa & Wyłupek, Grzegorz, 2014. "Validation of positive quadrant dependence," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 38-47.
    2. Bhattacharyya, Dhrubasish & Khan, Ruhul Ali & Mitra, Murari, 2021. "Tests for Laplace order dominance with applications to insurance data," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 163-173.

    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. Dehejia Vivek H. & Voia Marcel C., 2012. "International Income Comparisons and Social Welfare: Methodology, Analysis, and Implications," Journal of Globalization and Development, De Gruyter, vol. 3(1), pages 1-24, June.
    2. M. Azhar Hussain & Nikolaj Siersbæk & Lars Peter Østerdal, 2020. "Multidimensional welfare comparisons of EU member states before, during, and after the financial crisis: a dominance approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 645-686, December.
    3. 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.
    4. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    5. Stengos, Thanasis & Thompson, Brennan S., 2012. "Testing for bivariate stochastic dominance using inequality restrictions," Economics Letters, Elsevier, vol. 115(1), pages 60-62.
    6. 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.
    7. 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.
    8. 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.
    9. Olmo, José, 2008. "Testing downside risk efficiency under market distress," UC3M Working papers. Economics we084321, Universidad Carlos III de Madrid. Departamento de Economía.
    10. 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.
    11. Olmo, José, 2009. "Downside Risk Efficiency Under Market Distress," UC3M Working papers. Economics we094423, Universidad Carlos III de Madrid. Departamento de Economía.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Brendan K. Beare & Jackson D. Clarke, 2022. "Modified Wilcoxon-Mann-Whitney tests of stochastic dominance," Papers 2210.08892, arXiv.org.
    17. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Wang, 2002. "Consistent testing for stochastic dominance: a subsampling approach," CeMMAP working papers 03/02, Institute for Fiscal Studies.
    18. Hooi Hooi Lean & Michael McAleer & Wing-Keung Wong, 2013. "Risk-averse and Risk-seeking Investor Preferences for Oil Spot and Futures," Documentos de Trabajo del ICAE 2013-31, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Aug 2013.
    19. Maasoumi, Esfandiar & Almas Heshmati, 2003. "Evaluating Dominance Ranking of PSID Incomes by various Household Attributes," Departmental Working Papers 0509, Southern Methodist University, Department of Economics.
    20. Grönqvist, Charlotta, 2009. "Empirical studies on the private value of Finnish patents," Bank of Finland Scientific Monographs, Bank of Finland, volume 0, number sm2009_041, March.

    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:21:y:2012:i:4:p:730-756. 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.