IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v119y2016icp317-325.html
   My bibliography  Save this article

Double asymptotics for the chi-square statistic

Author

Listed:
  • Rempała, Grzegorz A.
  • Wesołowski, Jacek

Abstract

We consider distributional limit of the Pearson chi-square statistic when the number of classes mn increases with the sample size n and n/mn→λ. Under mild moment conditions, the limit is Gaussian for λ=∞, Poisson for finite λ>0, and degenerate for λ=0.

Suggested Citation

  • Rempała, Grzegorz A. & Wesołowski, Jacek, 2016. "Double asymptotics for the chi-square statistic," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 317-325.
    • Handle: RePEc:eee:stapro:v:119:y:2016:i:c:p:317-325
    DOI: 10.1016/j.spl.2016.09.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715216301699
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2016.09.004?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. M. L. Menéndez & D. Morales & L. Pardo & I. Vajda, 1998. "Asymptotic distributions of φ‐divergences of hypothetical and observed frequencies on refined partitions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 71-89, March.
    2. Maciej Pietrzak & Grzegorz A. Rempała & Michał Seweryn & Jacek Wesołowski, 2016. "Limit theorems for empirical Rényi entropy and divergence with applications to molecular diversity analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 654-673, December.
    3. Morales, D. & Pardo, L. & Vajda, I., 2003. "Asymptotic laws for disparity statistics in product multinomial models," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 335-360, May.
    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. Agnieszka M Borys & Michał Seweryn & Tomasz Gołąbek & Łukasz Bełch & Agnieszka Klimkowska & Justyna Totoń-Żurańska & Julita Machlowska & Piotr Chłosta & Krzysztof Okoń & Paweł P Wołkow, 2019. "Patterns of gene expression characterize T1 and T3 clear cell renal cell carcinoma subtypes," PLOS ONE, Public Library of Science, vol. 14(5), pages 1-19, May.
    2. Morales, D. & Pardo, L. & Vajda, I., 2003. "Asymptotic laws for disparity statistics in product multinomial models," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 335-360, May.
    3. Broniatowski, Michel & Keziou, Amor, 2009. "Parametric estimation and tests through divergences and the duality technique," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 16-36, January.
    4. Györfi, L. & Vajda, I., 2002. "Asymptotic distributions for goodness-of-fit statistics in a sequence of multinomial models," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 57-67, January.
    5. W. V. Félix de Lima & A. D. C. Nascimento & G. J. A. Amaral, 2021. "Entropy-based pivotal statistics for multi-sample problems in planar shape," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 153-178, 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:eee:stapro:v:119:y:2016:i:c:p:317-325. 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.