IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v10y2008i3d10.1007_s11009-007-9054-2.html
   My bibliography  Save this article

Minimum Φ-Divergence Estimator and Φ-Divergence Statistics in Generalized Linear Models with Binary Data

Author

Listed:
  • J. A. Pardo

    (Complutense University of Madrid)

  • M. C. Pardo

    (Complutense University of Madrid)

Abstract

In this paper, we assume that the data are distributed according to a binomial distribution whose probabilities follow a generalized linear model. To fit the data the minimum φ-divergence estimator is studied as a generalization of the maximum likelihood estimator. We use the minimum φ-divergence estimator, which is the basis of some new statistics, for solving the problems of testing in a generalized linear model with binary data. A wide simulation study is carried out for studying the behavior of the new family of estimators as well as of the new family of test statistics.

Suggested Citation

  • J. A. Pardo & M. C. Pardo, 2008. "Minimum Φ-Divergence Estimator and Φ-Divergence Statistics in Generalized Linear Models with Binary Data," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 357-379, September.
  • Handle: RePEc:spr:metcap:v:10:y:2008:i:3:d:10.1007_s11009-007-9054-2
    DOI: 10.1007/s11009-007-9054-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-007-9054-2
    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/s11009-007-9054-2?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. Pardo, M. C., 1999. "On Burbea-Rao Divergence Based Goodness-of-Fit Tests for Multinomial Models," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 65-87, April.
    2. M.L. Menéndez & J.A. Pardo & L. Pardo, 2003. "Theory & Methods: Tests for Bivariate Symmetry Against Ordered Alternatives in Square Contingency Tables," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(1), pages 115-123, March.
    3. Munoz-Garcia, J. & Munoz-Pichardo, J.M. & Pardo, L., 2006. "Cressie and Read power-divergences as influence measures for logistic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3199-3221, July.
    4. Morales, D. & Pardo, L. & Vajda, I., 1997. "Some New Statistics for Testing Hypotheses in Parametric Models, ," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 137-168, July.
    5. Konstantinos Fokianos, 2002. "Power Divergence Family of Tests for Categorical Time Series Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 543-564, September.
    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. Martín, N. & Balakrishnan, N., 2013. "Hypothesis testing in a generic nesting framework for general distributions," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 1-23.
    2. De Gregorio, A. & Iacus, S.M., 2013. "On a family of test statistics for discretely observed diffusion processes," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 292-316.
    3. 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.
    4. Alessandro DE GREGORIO & Stefano Maria IACUS, 2011. "On a family of test statistics for discretely observed diffusion processes," Departmental Working Papers 2011-37, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    5. Leorato, S., 2009. "A refined Jensen's inequality in Hilbert spaces and empirical approximations," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1044-1060, May.
    6. Broniatowski, M. & Leorato, S., 2006. "An estimation method for the Neyman chi-square divergence with application to test of hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1409-1436, July.
    7. Nada M. Alfaer & Ahmed M. Gemeay & Hassan M. Aljohani & Ahmed Z. Afify, 2021. "The Extended Log-Logistic Distribution: Inference and Actuarial Applications," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    8. J. M. Muñoz-Pichardo & J. L. Moreno-Rebollo & R. Pino-Mejías & M. D. Cubiles Vega, 2019. "Influence measures in beta regression models through distance between distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 163-185, June.
    9. Martín, Nirian & Balakrishnan, Narayanaswami, 2011. "Hypothesis testing in a generic nesting framework with general population distributions," DES - Working Papers. Statistics and Econometrics. WS ws113527, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Munoz-Garcia, J. & Munoz-Pichardo, J.M. & Pardo, L., 2006. "Cressie and Read power-divergences as influence measures for logistic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3199-3221, July.
    11. N. Martín & L. Pardo & K. Zografos, 2019. "On divergence tests for composite hypotheses under composite likelihood," Statistical Papers, Springer, vol. 60(6), pages 1883-1919, December.
    12. Alessandro DE GREGORIO & Stefano Maria IACUS, 2009. "Pseudo phi-divergence test statistics and multidimensional Ito processes," Departmental Working Papers 2009-48, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    13. Basu, Ayanendranath & Chakraborty, Soumya & Ghosh, Abhik & Pardo, Leandro, 2022. "Robust density power divergence based tests in multivariate analysis: A comparative overview of different approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    14. Ahmed Z. Afify & Ahmed M. Gemeay & Noor Akma Ibrahim, 2020. "The Heavy-Tailed Exponential Distribution: Risk Measures, Estimation, and Application to Actuarial Data," Mathematics, MDPI, vol. 8(8), pages 1-28, August.
    15. A. Gregorio & S. M. Iacus, 2019. "Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 233-261, July.
    16. Chalabi, Yohan & Wuertz, Diethelm, 2012. "Portfolio optimization based on divergence measures," MPRA Paper 43332, University Library of Munich, Germany.
    17. B. Abraham & P. Sankaran, 2006. "Renyi's entropy for residual lifetime distribution," Statistical Papers, Springer, vol. 47(1), pages 17-29, 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:spr:metcap:v:10:y:2008:i:3:d:10.1007_s11009-007-9054-2. 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.