IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v112y2012icp130-144.html
   My bibliography  Save this article

Nonparametric bootstrap tests of conditional independence in two-way contingency tables

Author

Listed:
  • Hui, Francis K.C.
  • Geenens, Gery

Abstract

When analyzing a two-way contingency table, a preliminary question is often whether the categorical variables under study, say R and S, are independent or not. Suppose now that for each individual in the table, a continuous variable X is also known. It is then worth analyzing the table conditionally on X. Contrasting these “local” results to the global unconditional case allows one to go beyond the initial analysis and provide a better understanding of the underlying phenomenon. Recently, Geenens and Simar (2010) [11] have proposed two nonparametric procedures for testing whether R and S are conditionally independent given X, free of any constraining linearity assumptions. However, based on an average of kernel-based estimators, the asymptotic criterion they suggested shows an inflated Type I error (false positive) for small to moderate sample sizes. In this paper, we address this problem by proposing consistent bootstrap versions of the Geenens–Simar test procedures when testing for local independence. A comprehensive simulation study indeed shows the superiority of the bootstrap rejection criterion as compared to the asymptotic criterion in terms of Type I error. It also highlights the advantage of the flexibility guaranteed by the nonparametric Geenens–Simar tests when compared with parametric competitors, e.g. logistic models. The approach is finally illustrated with a real-data example.

Suggested Citation

  • Hui, Francis K.C. & Geenens, Gery, 2012. "Nonparametric bootstrap tests of conditional independence in two-way contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 130-144.
  • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:130-144
    DOI: 10.1016/j.jmva.2012.05.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12001418
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2012.05.015?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. Romano, Joseph P. & Wolf, Michael, 2000. "A more general central limit theorem for m-dependent random variables with unbounded m," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 115-124, April.
    2. Marozzi, Marco, 2004. "A bi-aspect nonparametric test for the multi-sample location problem," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 81-92, May.
    3. Horowitz, Joel L., 2001. "The bootstrap and hypothesis tests in econometrics," Journal of Econometrics, Elsevier, vol. 100(1), pages 37-40, January.
    4. Marozzi, Marco, 2004. "A bi-aspect nonparametric test for the two-sample location problem," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 639-648, January.
    5. Geenens, Gery & Simar, Léopold, 2010. "Nonparametric tests for conditional independence in two-way contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 765-788, April.
    6. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228, Elsevier.
    7. Härdle, Wolfgang & Horowitz, Joel L. & Kreiss, Jens-Peter, 2001. "Bootstrap methods for time series," SFB 373 Discussion Papers 2001,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Rodriguez-Campos, M. C. & Cao-Abad, R., 1993. "Nonparametric bootstrap confidence intervals for discrete regression functions," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 207-222, July.
    9. Brombin, Chiara & Salmaso, Luigi, 2009. "Multi-aspect permutation tests in shape analysis with small sample size," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3921-3931, October.
    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. Gustavo J. Bobonis & Paul J. Gertler & Marco Gonzalez-Navarro & Simeon Nichter, 2022. "Vulnerability and Clientelism," American Economic Review, American Economic Association, vol. 112(11), pages 3627-3659, November.
    2. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    3. Benjamin Faber & Thibault Fally, 2022. "Firm Heterogeneity in Consumption Baskets: Evidence from Home and Store Scanner Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(3), pages 1420-1459.
    4. Benjamin Faber & Cecile Gaubert, 2019. "Tourism and Economic Development: Evidence from Mexico's Coastline," American Economic Review, American Economic Association, vol. 109(6), pages 2245-2293, June.
    5. Perez, Victor, 2015. "Moving in and out of poverty in Mexico: What can we learn from pseudo-panel methods?," ISER Working Paper Series 2015-16, Institute for Social and Economic Research.
    6. Götz, Thomas B. & Hecq, Alain & Smeekes, Stephan, 2016. "Testing for Granger causality in large mixed-frequency VARs," Journal of Econometrics, Elsevier, vol. 193(2), pages 418-432.
    7. Orth, Walter, 2012. "The predictive accuracy of credit ratings: Measurement and statistical inference," International Journal of Forecasting, Elsevier, vol. 28(1), pages 288-296.
    8. Le, Vo Phuong Mai & Meenagh, David & Minford, Patrick & Wickens, Michael, 2011. "How much nominal rigidity is there in the US economy? Testing a new Keynesian DSGE model using indirect inference," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2078-2104.
    9. Li, Jia & Todorov, Viktor & Tauchen, George & Chen, Rui, 2017. "Mixed-scale jump regressions with bootstrap inference," Journal of Econometrics, Elsevier, vol. 201(2), pages 417-432.
    10. Sevan Gulesserian & Mohitosh Kejriwal, 2014. "On the power of bootstrap tests for stationarity: a Monte Carlo comparison," Empirical Economics, Springer, vol. 46(3), pages 973-998, May.
    11. A. Talha Yalta, 2016. "Bootstrap Inference of Level Relationships in the Presence of Serially Correlated Errors: A Large Scale Simulation Study and an Application in Energy Demand," Computational Economics, Springer;Society for Computational Economics, vol. 48(2), pages 339-366, August.
    12. Grammig, Joachim & Küchlin, Eva-Maria, 2017. "A two-step indirect inference approach to estimate the long-run risk asset pricing model," CFS Working Paper Series 572, Center for Financial Studies (CFS).
    13. Grammig, Joachim & Küchlin, Eva-Maria, 2017. "A two-step indirect inference approach to estimate the long-run risk asset pricing model," CFR Working Papers 17-01, University of Cologne, Centre for Financial Research (CFR).
    14. Rourke, Thomas, 2014. "The delta- and vega-related information content of near-the-money option market trading activity," Journal of Financial Markets, Elsevier, vol. 20(C), pages 175-193.
    15. Puente-Ajovín, Miguel & Sanso-Navarro, Marcos, 2015. "Granger causality between debt and growth: Evidence from OECD countries," International Review of Economics & Finance, Elsevier, vol. 35(C), pages 66-77.
    16. Huang, Zhendong & Ferrari, Davide & Qian, Guoqi, 2017. "Parsimonious and powerful composite likelihood testing for group difference and genotype–phenotype association," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 37-49.
    17. Saqib Aziz & Michael Dowling & Jean-Jacques Lilti, 2016. "Bank Acquisitiveness and Financial Crisis Vulnerability," Post-Print hal-01393953, HAL.
    18. Chang, Hung-Hao & Mishra, Ashok K. & Livingston, Michael, 2011. "Agricultural policy and its impact on fuel usage: Empirical evidence from farm household analysis," Applied Energy, Elsevier, vol. 88(1), pages 348-353, January.
    19. Hardwick Tchale & Johannes Sauer, 2007. "The efficiency of maize farming in Malawi. A bootstrapped translog frontier," Post-Print hal-01201145, HAL.
    20. Lee, Tae-Hwy & Tu, Yundong & Ullah, Aman, 2014. "Nonparametric and semiparametric regressions subject to monotonicity constraints: Estimation and forecasting," Journal of Econometrics, Elsevier, vol. 182(1), pages 196-210.

    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:jmvana:v:112:y:2012:i:c:p:130-144. 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.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.