IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v31y2022i1d10.1007_s11749-021-00769-9.html
   My bibliography  Save this article

Testing the equality of a large number of populations

Author

Listed:
  • M. D. Jiménez-Gamero

    (Universidad de Sevilla)

  • M. Cousido-Rocha

    (Universidad de Vigo)

  • M. V. Alba-Fernández

    (Universidad de Jaén)

  • F. Jiménez-Jiménez

    (Universidad de Jaén)

Abstract

Given k independent samples with finite but arbitrary dimension, this paper deals with the problem of testing for the equality of their distributions that can be continuous, discrete or mixed. In contrast to the classical setting where k is assumed to be fixed and the sample size from each population increases without bound, here k is assumed to be large and the size of each sample is either bounded or small in comparison with k. The asymptotic distribution of two test statistics is stated under the null hypothesis of the equality of the k distributions as well as under alternatives, which let us to study the asymptotic power of the resulting tests. Specifically, it is shown that both test statistics are asymptotically free distributed under the null hypothesis. The finite sample performance of the tests based on the asymptotic null distribution is studied via simulation. An application of the proposal to a real data set is included. The use of the proposed procedure for infinite dimensional data, as well as other possible extensions, are discussed.

Suggested Citation

  • M. D. Jiménez-Gamero & M. Cousido-Rocha & M. V. Alba-Fernández & F. Jiménez-Jiménez, 2022. "Testing the equality of a large number of populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 1-21, March.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:1:d:10.1007_s11749-021-00769-9
    DOI: 10.1007/s11749-021-00769-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-021-00769-9
    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/s11749-021-00769-9?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. Mollick, Ethan, 2014. "The dynamics of crowdfunding: An exploratory study," Journal of Business Venturing, Elsevier, vol. 29(1), pages 1-16.
    2. Ajay Agrawal & Christian Catalini & Avi Goldfarb, 2014. "Some Simple Economics of Crowdfunding," Innovation Policy and the Economy, University of Chicago Press, vol. 14(1), pages 63-97.
    3. D. Zhan & J. D. Hart, 2014. "Testing equality of a large number of densities," Biometrika, Biometrika Trust, vol. 101(2), pages 449-464.
    4. R. Bárcenas & J. Ortega & A. J. Quiroz, 2017. "Quadratic forms of the empirical processes for the two-sample problem for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 503-526, September.
    5. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
    6. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    7. Marta Cousido-Rocha & Jacobo Uña-Álvarez & Jeffrey D. Hart, 2019. "Testing equality of a large number of densities under mixing conditions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1203-1228, December.
    8. Jiménez-Gamero, M.D. & Alba-Fernández, M.V. & Jodrá, P. & Barranco-Chamorro, I., 2017. "Fast tests for the two-sample problem based on the empirical characteristic function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 390-410.
    9. Marie Hušková & Simos Meintanis, 2008. "Tests for the multivariate -sample problem based on the empirical characteristic function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 263-277.
    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. Christian Acal & Ana M. Aguilera, 2023. "Basis expansion approaches for functional analysis of variance with repeated measures," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 291-321, June.
    2. Alba-Fernández, M.V. & Jiménez-Gamero, M.D. & Jiménez-Jiménez, F., 2024. "Testing for proportions when data are classified into a large number of groups," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 588-600.

    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. Dolores & Franco-Pereira, Alba M., 2021. "Testing the equality of a large number of means of functional data," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Cousido-Rocha, Marta & de Uña-Álvarez, Jacobo & Hart, Jeffrey D., 2019. "A two-sample test for the equality of univariate marginal distributions for high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    3. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    4. Wesemann, Henrik & Wincent, Joakim, 2021. "A whole new world: Counterintuitive crowdfunding insights for female founders," Journal of Business Venturing Insights, Elsevier, vol. 15(C).
    5. Chul Kim & P. K. Kannan & Michael Trusov & Andrea Ordanini, 2020. "Modeling Dynamics in Crowdfunding," Marketing Science, INFORMS, vol. 39(2), pages 339-365, March.
    6. Appio, Francesco Paolo & Leone, Daniele & Platania, Federico & Schiavone, Francesco, 2020. "Why are rewards not delivered on time in rewards-based crowdfunding campaigns? An empirical exploration," Technological Forecasting and Social Change, Elsevier, vol. 157(C).
    7. Tuo Gladys & Yi Feng & Sarpong Solomon & Wang Wenxin, 2020. "The Second Round Resource Acquisition of Entrepreneurial Crowdfunded Ventures: The Relevance of Campaign and Project Implementation Performance Outcomes," Entrepreneurship Research Journal, De Gruyter, vol. 10(3), pages 1-21, July.
    8. Jung, Eunjun & Lee, Changjun & Hwang, Junseok, 2022. "Effective strategies to attract crowdfunding investment based on the novelty of business ideas," Technological Forecasting and Social Change, Elsevier, vol. 178(C).
    9. Zunino, Diego & van Praag, Mirjam C. & Dushnitsky, Gary, 2017. "Badge of Honor or Scarlet Letter? Unpacking Investors' Judgment of Entrepreneurs' Past Failure," IZA Discussion Papers 11017, Institute of Labor Economics (IZA).
    10. Tafesse, Wondwesen, 2021. "Communicating crowdfunding campaigns: How message strategy, vivid media use and product type influence campaign success," Journal of Business Research, Elsevier, vol. 127(C), pages 252-263.
    11. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2020. "Change-point methods for multivariate time-series: paired vectorial observations," Statistical Papers, Springer, vol. 61(4), pages 1351-1383, August.
    12. Sylvain Dejean, 2019. "The role of distance and social networks in the geography of crowdfunding: evidence from France," Working Papers hal-01645147, HAL.
    13. Roland Strausz, 2017. "A Theory of Crowdfunding: A Mechanism Design Approach with Demand Uncertainty and Moral Hazard," American Economic Review, American Economic Association, vol. 107(6), pages 1430-1476, June.
    14. Damien Besancenot & Radu Vranceanu, 2018. "Crowdfunding with overenthusiastic investors : a global game model," Working Papers hal-01718793, HAL.
    15. Saul Estrin & Susanna Khavul & Mike Wright, 2022. "Soft and hard information in equity crowdfunding: network effects in the digitalization of entrepreneurial finance," Small Business Economics, Springer, vol. 58(4), pages 1761-1781, April.
    16. Estrin, Saul & Gozman, Daniel & Khavul, Susanna, 2017. "Equity crowdfunding and early stage entrepreneurial finance: damaging or disruptive?," LSE Research Online Documents on Economics 86590, London School of Economics and Political Science, LSE Library.
    17. Mahmood, Ammara & Luffarelli, Jonathan & Mukesh, Mudra, 2019. "What's in a logo? The impact of complex visual cues in equity crowdfunding," Journal of Business Venturing, Elsevier, vol. 34(1), pages 41-62.
    18. Bergmann, Ariel & Burton, Bruce & Klaes, Matthias, 2021. "European perceptions on crowdfunding for renewables: Positivity and pragmatism," Ecological Economics, Elsevier, vol. 179(C).
    19. Andreas Wald & Merete Holmesland & Kalanit Efrat, 2019. "It Is Not All About Money: Obtaining Additional Benefits Through Equity Crowdfunding," Journal of Entrepreneurship and Innovation in Emerging Economies, Entrepreneurship Development Institute of India, vol. 28(2), pages 270-294, September.
    20. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.

    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:31:y:2022:i:1:d:10.1007_s11749-021-00769-9. 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.