IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v81y2011i10p1978-1990.html
   My bibliography  Save this article

Estimating Rao’s statistic distribution for testing uniform association in cross-classifications

Author

Listed:
  • Alba-Fernández, V.
  • Jiménez-Gamero, M.D.

Abstract

We consider the problem of testing uniform association in cross-classifications with ordered categories taking as test statistic a Rϕ divergence. The asymptotic null distribution of any test statistic in this class is not free because it depends on the unknown true vector of probabilities, so in practice one has to approximate it in order to get an estimate of the null distribution. As an alternative approach we propose to approximate the null distribution of the test statistic by bootstrapping. We show that the bootstrap yields a consistent null distribution estimator. The finite sample performance of the bootstrap estimator is studied by simulation. We also compare it empirically with the asymptotic null approximation. From the simulations it can be concluded that it is worth calculating the bootstrap estimator, because it is more accurate than the approximation yielded by the asymptotic null distribution which, furthermore, cannot always be exactly computed. Finally, the results are applied to some real data sets.

Suggested Citation

  • Alba-Fernández, V. & Jiménez-Gamero, M.D., 2011. "Estimating Rao’s statistic distribution for testing uniform association in cross-classifications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 1978-1990.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:10:p:1978-1990
    DOI: 10.1016/j.matcom.2011.01.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475411000541
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2011.01.014?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. Y. Fujikoshi, 1977. "An asymptotic expansion for the distributions of the latent roots of the Wishart matrix with multiple population roots," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 379-387, December.
    2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    3. Tomizawa, Sadao, 1991. "Shannon entropy type measure of departure from uniform association in cross-classifications having ordered categories," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 547-550, June.
    Full references (including those not matched with items on IDEAS)

    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. Jiménez-Gamero, M.D. & Alba-Fernández, M.V. & Estudillo-Martínez, M.D., 2014. "Burbea–Rao divergence based statistics for testing uniform association," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 1-18.
    2. M. Jiménez-Gamero & R. Pino-Mejías & A. Rufián-Lizana, 2014. "Minimum $$K_{\phi }$$ K ϕ -divergence estimators for multinomial models and applications," Computational Statistics, Springer, vol. 29(1), pages 363-401, February.
    3. P.A.V.B. Swamy & I-Lok Chang & Jatinder S. Mehta & William H. Greene & Stephen G. Hall & George S. Tavlas, 2016. "Removing Specification Errors from the Usual Formulation of Binary Choice Models," Econometrics, MDPI, vol. 4(2), pages 1-21, June.
    4. Carlo Altavilla & Raffaella Giacomini & Giuseppe Ragusa, 2017. "Anchoring the yield curve using survey expectations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1055-1068, September.
    5. Fernando Rios-Avila & Gustavo Canavire-Bacarreza, 2018. "Standard-error correction in two-stage optimization models: A quasi–maximum likelihood estimation approach," Stata Journal, StataCorp LP, vol. 18(1), pages 206-222, March.
    6. Sandy Fréret & Denis Maguain, 2017. "The effects of agglomeration on tax competition: evidence from a two-regime spatial panel model on French data," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(6), pages 1100-1140, December.
    7. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    8. Gregory, Allan W. & McCurdy, Thomas H., 1986. "The unbiasedness hypothesis in the forward foreign exchange market: A specification analysis with application to France, Italy, Japan, the United Kingdom and West Germany," European Economic Review, Elsevier, vol. 30(2), pages 365-381, April.
    9. B. Praag & T. Dijkstra & J. Velzen, 1985. "Least-squares theory based on general distributional assumptions with an application to the incomplete observations problem," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 25-36, March.
    10. Reischmann, Markus, 2016. "Creative accounting and electoral motives: Evidence from OECD countries," Journal of Comparative Economics, Elsevier, vol. 44(2), pages 243-257.
    11. Czudaj Robert L., 2020. "The role of uncertainty on agricultural futures markets momentum trading and volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(3), pages 1-39, June.
    12. Vassilios Babalos & Mehmet Balcilar & Rangan Gupta, 2014. "Revisiting Herding Behavior in REITs: A Regime-Switching Approach," Working Papers 201448, University of Pretoria, Department of Economics.
    13. Topi Miettinen & Sigrid Suetens, 2008. "Communication and Guilt in a Prisoner's Dilemma," Journal of Conflict Resolution, Peace Science Society (International), vol. 52(6), pages 945-960, December.
    14. Towfiqul Islam Khan & Mashfique Ibne Akbar, 2015. "Illicit Financial Flow in view of Financing the Post-2015 Development Agenda," Southern Voice Occasional Paper 25, Southern Voice.
    15. Catherine Doz & Domenico Giannone & Lucrezia Reichlin, 2012. "A Quasi–Maximum Likelihood Approach for Large, Approximate Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1014-1024, November.
    16. Potrafke, Niklas, 2019. "Electoral cycles in perceived corruption: International empirical evidence," Journal of Comparative Economics, Elsevier, vol. 47(1), pages 215-224.
    17. Corradi, Valentina & Swanson, Norman R., 2004. "A test for the distributional comparison of simulated and historical data," Economics Letters, Elsevier, vol. 85(2), pages 185-193, November.
    18. Hendrik Thiel & Stephan L. Thomsen, 2015. "Individual Poverty Paths and the Stability of Control-Perception," SOEPpapers on Multidisciplinary Panel Data Research 794, DIW Berlin, The German Socio-Economic Panel (SOEP).
    19. Arzheimer, Kai & Evans, Jocelyn, 2010. "Bread and butter à la française: Multiparty forecasts of the French legislative vote (1981-2007)," International Journal of Forecasting, Elsevier, vol. 26(1), pages 19-31, January.
    20. repec:ebl:ecbull:v:3:y:2008:i:5:p:1-7 is not listed on IDEAS
    21. Tobias Hartl & Roland Jucknewitz, 2022. "Approximate state space modelling of unobserved fractional components," Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 75-98, January.

    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:eee:matcom:v:81:y:2011:i:10:p:1978-1990. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.