IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v55y2014i3p643-652.html
   My bibliography  Save this article

Covariance matrix of the bias-corrected maximum likelihood estimator in generalized linear models

Author

Listed:
  • Gauss Cordeiro
  • Denise Botter
  • Alexsandro Cavalcanti
  • Lúcia Barroso

Abstract

For the first time, we obtain a general formula for the $$n^{-2}$$ asymptotic covariance matrix of the bias-corrected maximum likelihood estimators of the linear parameters in generalized linear models, where $$n$$ is the sample size. The usefulness of the formula is illustrated in order to obtain a better estimate of the covariance of the maximum likelihood estimators and to construct better Wald statistics. Simulation studies and an application support our theoretical results. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Gauss Cordeiro & Denise Botter & Alexsandro Cavalcanti & Lúcia Barroso, 2014. "Covariance matrix of the bias-corrected maximum likelihood estimator in generalized linear models," Statistical Papers, Springer, vol. 55(3), pages 643-652, August.
  • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:643-652
    DOI: 10.1007/s00362-013-0514-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-013-0514-1
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00362-013-0514-1?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. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    2. Cordeiro, Gauss M., 2004. "Second-order covariance matrix of maximum likelihood estimates in generalized linear models," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 153-160, January.
    3. Audrey Cysneiros & Katya Rodrigues & Gauss Cordeiro & Silvia Ferrari, 2010. "Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models," Statistical Papers, Springer, vol. 51(2), pages 273-284, June.
    4. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    5. Ferrari, Silvia L. P. & Botter, Denise A. & Cordeiro, Gauss M. & Cribari-Neto, Francisco, 1996. "Second- and third-order bias reduction for one-parameter family models," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 339-345, November.
    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. Dries P.J. Kuijper & Jakub W. Bubnicki & Marcin Churski & Bjorn Mols & Pim van Hooft, 2015. "Context dependence of risk effects: wolves and tree logs create patches of fear in an old-growth forest," Behavioral Ecology, International Society for Behavioral Ecology, vol. 26(6), pages 1558-1568.
    2. Guillermo Martínez-Flórez & Artur J. Lemonte & Germán Moreno-Arenas & Roger Tovar-Falón, 2022. "The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    3. Lucio Masserini & Matilde Bini & Monica Pratesi, 2017. "Effectiveness of non-selective evaluation test scores for predicting first-year performance in university career: a zero-inflated beta regression approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 693-708, March.
    4. Silvia Noirjean & Mario Biggeri & Laura Forastiere & Fabrizia Mealli & Maria Nannini, 2023. "Estimating causal effects of community health financing via principal stratification," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1317-1350, October.
    5. Maria Gheorghe & Susan Picavet & Monique Verschuren & Werner B. F. Brouwer & Pieter H. M. Baal, 2017. "Health losses at the end of life: a Bayesian mixed beta regression approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 723-749, June.
    6. Ehsan Bahrami Samani & Elham Tabrizi, 2023. "Joint Linear Modeling of Mixed Data and Its Application to Email Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 175-209, May.
    7. Murilo Wohlgemuth & Carlos Ernani Fries & Ângelo Márcio Oliveira Sant’Anna & Ricardo Giglio & Diego Castro Fettermann, 2020. "Assessment of the technical efficiency of Brazilian logistic operators using data envelopment analysis and one inflated beta regression," Annals of Operations Research, Springer, vol. 286(1), pages 703-717, March.
    8. Yury R. Benites & Vicente G. Cancho & Edwin M. M. Ortega & Roberto Vila & Gauss M. Cordeiro, 2022. "A New Regression Model on the Unit Interval: Properties, Estimation, and Application," Mathematics, MDPI, vol. 10(17), pages 1-17, September.
    9. Kathryn M. Irvine & T. J. Rodhouse & Ilai N. Keren, 2016. "Extending Ordinal Regression with a Latent Zero-Augmented Beta Distribution," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 619-640, December.
    10. Guillermo Martínez-Flórez & Roger Tovar-Falón & Carlos Barrera-Causil, 2022. "Inflated Unit-Birnbaum-Saunders Distribution," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    11. Hildete P. Pinheiro & Rafael P. Maia & Eufrásio A. Lima Neto & Mariana Rodrigues-Motta, 2019. "Zero-one augmented beta and zero-inflated discrete models with heterogeneous dispersion for the analysis of student academic performance," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 749-767, December.
    12. Maria Gheorghe & Werner Brouwer & Pieter Baal, 2015. "Did the health of the Dutch population improve between 2001 and 2008? Investigating age- and gender-specific trends in quality of life," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 16(8), pages 801-811, November.
    13. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.
    14. Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
    15. Raffaele Brancati & Emanuela Marrocu & Manuel Romagnoli & Stefano Usai, 2018. "Innovation activities and learning processes in the crisis: evidence from Italian export in manufacturing and services," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 27(1), pages 107-130.
    16. Guillermo Martínez-Flórez & Heleno Bolfarine & Héctor Gómez, 2015. "Doubly censored power-normal regression models with inflation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 265-286, June.
    17. Oscar Melo & Carlos Melo & Jorge Mateu, 2015. "Distance-based beta regression for prediction of mutual funds," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 83-106, January.
    18. Guillermo Martínez-Flórez & Roger Tovar-Falón & Víctor Leiva & Cecilia Castro, 2024. "Skew-Normal Inflated Models: Mathematical Characterization and Applications to Medical Data with Excess of Zeros and Ones," Mathematics, MDPI, vol. 12(16), pages 1-23, August.
    19. Luca Scrucca, 2022. "A COVINDEX based on a GAM beta regression model with an application to the COVID-19 pandemic in Italy," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 881-900, October.
    20. Ruey-Ching Hwang & Huimin Chung & C. K. Chu, 2016. "A Two-Stage Probit Model for Predicting Recovery Rates," Journal of Financial Services Research, Springer;Western Finance Association, vol. 50(3), pages 311-339, December.

    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:stpapr:v:55:y:2014:i:3:p:643-652. 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.