IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v80y2017i2d10.1007_s00184-016-0596-6.html
   My bibliography  Save this article

A new approach to distribution free tests in contingency tables

Author

Listed:
  • Thuong T. M. Nguyen

    (Victoria University of Wellington)

Abstract

We suggest an extremely wide class of asymptotically distribution free goodness of fit tests for testing independence in two-way contingency tables, or equivalently, independence of two discrete random variables. The nature of these tests is that the test statistics can be viewed as definite functions of the transformation of $$\widehat{T}_n = (\widehat{T}_{ij})=\Big (\frac{\nu _{ij}- n\hat{a}_i\hat{b}_j}{\sqrt{n\hat{a}_i\hat{b}_j}}\Big )$$ T ^ n = ( T ^ i j ) = ( ν i j - n a ^ i b ^ j n a ^ i b ^ j ) where $$\nu _{ij}$$ ν i j are frequencies and $$\hat{a}_i, \hat{b}_j$$ a ^ i , b ^ j are estimated marginal distributions. Our method is also applicable for testing independence of two discrete random vectors. We make some comparisons on statistical powers of the new tests with the conventional chi-square test and suggest some cases in which this class is significantly more powerful.

Suggested Citation

  • Thuong T. M. Nguyen, 2017. "A new approach to distribution free tests in contingency tables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 153-170, February.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:2:d:10.1007_s00184-016-0596-6
    DOI: 10.1007/s00184-016-0596-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-016-0596-6
    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/s00184-016-0596-6?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. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, 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. Estate V. Khmaladze, 2021. "Distribution-free testing in linear and parametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1063-1087, December.
    2. Roberts, Leigh A., 2019. "Distribution free goodness of fit testing of grouped Bernoulli trials," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 47-53.
    3. Khmaladze, Estate, 2017. "Distribution free testing for conditional distributions given covariates," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 348-354.

    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. Kasy, Maximilian, 2011. "A nonparametric test for path dependence in discrete panel data," Economics Letters, Elsevier, vol. 113(2), pages 172-175.
    2. Atı̇la Abdulkadı̇roğlu & Joshua D. Angrist & Yusuke Narita & Parag Pathak, 2022. "Breaking Ties: Regression Discontinuity Design Meets Market Design," Econometrica, Econometric Society, vol. 90(1), pages 117-151, January.
    3. Ashesh Rambachan & Jonathan Roth, 2020. "Design-Based Uncertainty for Quasi-Experiments," Papers 2008.00602, arXiv.org, revised Feb 2024.
    4. Debashis Ghosh, 2004. "Semiparametric methods for the binormal model with multiple biomarkers," The University of Michigan Department of Biostatistics Working Paper Series 1046, Berkeley Electronic Press.
    5. Brian D. Williamson & Peter B. Gilbert & Marco Carone & Noah Simon, 2021. "Nonparametric variable importance assessment using machine learning techniques," Biometrics, The International Biometric Society, vol. 77(1), pages 9-22, March.
    6. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    7. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2018. "Asymptotic results under multiway clustering," Papers 1807.07925, arXiv.org, revised Aug 2018.
    8. Dominic Edelmann & Tobias Terzer & Donald Richards, 2021. "A Basic Treatment of the Distance Covariance," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 12-25, May.
    9. Stefano Caria & Grant Gordon & Maximilian Kasy & Simon Quinn & Soha Shami & Alexander Teytelboym, 2020. "An Adaptive Targeted Field Experiment: Job Search Assistance for Refugees in Jordan," CESifo Working Paper Series 8535, CESifo.
    10. repec:hal:spmain:info:hdl:2441/75dbbb2hc596np6q8flqf6i79k is not listed on IDEAS
    11. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    12. Abe, Toshihiro & Miyata, Yoichi & Shiohama, Takayuki, 2023. "Bayesian estimation for mode and anti-mode preserving circular distributions," Econometrics and Statistics, Elsevier, vol. 27(C), pages 136-160.
    13. Bryan S. Graham, 2017. "An econometric model of network formation with degree heterogeneity," CeMMAP working papers 08/17, Institute for Fiscal Studies.
    14. Benoumechiara Nazih & Bousquet Nicolas & Michel Bertrand & Saint-Pierre Philippe, 2020. "Detecting and modeling critical dependence structures between random inputs of computer models," Dependence Modeling, De Gruyter, vol. 8(1), pages 263-297, January.
    15. Zhang, Feipeng & Xu, Yixiong & Fan, Caiyun, 2023. "Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment," International Review of Financial Analysis, Elsevier, vol. 90(C).
    16. Arun G. Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2019. "Best Linear Approximations to Set Identified Functions: With an Application to the Gender Wage Gap," NBER Working Papers 25593, National Bureau of Economic Research, Inc.
    17. Yuan Liao & Anna Simoni, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," Papers 1212.3267, arXiv.org, revised Nov 2013.
    18. Kline, Patrick, 2014. "A note on variance estimation for the Oaxaca estimator of average treatment effects," Economics Letters, Elsevier, vol. 122(3), pages 428-431.
    19. Graham, Bryan S. & Hahn, Jinyong & Poirier, Alexandre & Powell, James L., 2018. "A quantile correlated random coefficients panel data model," Journal of Econometrics, Elsevier, vol. 206(2), pages 305-335.
    20. P. Čížek & S. Sadikoglu, 2018. "Bias-corrected quantile regression estimation of censored regression models," Statistical Papers, Springer, vol. 59(1), pages 215-247, March.
    21. Ting Ye & Ashkan Ertefaie & James Flory & Sean Hennessy & Dylan S. Small, 2023. "Instrumented difference‐in‐differences," Biometrics, The International Biometric Society, vol. 79(2), pages 569-581, June.

    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:metrik:v:80:y:2017:i:2:d:10.1007_s00184-016-0596-6. 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.