IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v82y2020i1d10.1007_s13571-018-0179-9.html
   My bibliography  Save this article

Improved Estimation for a New Class of Parametric Link Functions in Binary Regression

Author

Listed:
  • Artur J. Lemonte

    (Universidade Federal do Rio Grande no Norte)

  • Germán Moreno–Arenas

    (Universidad Industrial de Santander)

Abstract

We develop nearly unbiased maximum likelihood estimators for a new class of asymmetric link functions proposed recently in the statistic literature by Lemonte and Bazán (TEST 27, 597–617 2018). These authors have introduced a broad class of parametric link functions in binary regression that contains as special cases both symmetric as well as asymmetric links. We discuss maximum likelihood estimation for the model parameters and derive a closed-form expression for the second order bias of these estimators. The second order bias can be easily computed as an ordinary weighted least-squares regression and is then used to define bias corrected maximum likelihood estimators. Monte Carlo simulation experiments are conducted in order to investigate the performance of the corrected estimators. The numerical results reveal that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Empirical applications are considered for illustrative purposes.

Suggested Citation

  • Artur J. Lemonte & Germán Moreno–Arenas, 2020. "Improved Estimation for a New Class of Parametric Link Functions in Binary Regression," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 84-110, May.
    • Handle: RePEc:spr:sankhb:v:82:y:2020:i:1:d:10.1007_s13571-018-0179-9
    DOI: 10.1007/s13571-018-0179-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-018-0179-9
    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/s13571-018-0179-9?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. Patriota, Alexandre G. & Lemonte, Artur J., 2009. "Bias correction in a multivariate normal regression model with general parameterization," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1655-1662, August.
    2. Alexandre Patriota & Artur Lemonte & Heleno Bolfarine, 2011. "Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model," Statistical Papers, Springer, vol. 52(2), pages 455-467, May.
    3. Artur J. Lemonte & Jorge L. Bazán, 2018. "New links for binary regression: an application to coca cultivation in Peru," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 597-617, September.
    4. Sungduk Kim & Ming-Hui Chen & Dipak K. Dey, 2008. "Flexible generalized t-link models for binary response data," Biometrika, Biometrika Trust, vol. 95(1), pages 93-106.
    5. Cordeiro, Gauss M. & Botter, Denise A., 2001. "Second-order biases of maximum likelihood estimates in overdispersed generalized linear models," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 269-280, December.
    6. Jorge Luis Bazán & Óscar Millones, 2008. "Una clasificación de modelos de regresión binaria asimétrica: el uso del BAYES-PUCP en una aplicación sobre la decisión del cultivo ilícito de hoja de coca," Revista Economía, Fondo Editorial - Pontificia Universidad Católica del Perú, issue 62, pages 17-32.
    7. Cordeiro, Gauss M. & Vasconcellos, Klaus L. P., 1997. "Bias correction for a class of multivariate nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 155-164, September.
    8. Cordeiro, Gauss M. & Ferrari, Silvia L. P. & Uribe-Opazo, Miguel A. & Vasconcellos, Klaus L. P., 2000. "Corrected maximum-likelihood estimation in a class of symmetric nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 317-328, February.
    9. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    10. Daryl Pregibon, 1980. "Goodness of Link Tests for Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 15-24, March.
    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. Artur J. Lemonte & Jorge L. Bazán, 2018. "New links for binary regression: an application to coca cultivation in Peru," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 597-617, September.
    2. Patriota, Alexandre G. & Lemonte, Artur J., 2009. "Bias correction in a multivariate normal regression model with general parameterization," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1655-1662, August.
    3. Alexandre Patriota & Artur Lemonte & Heleno Bolfarine, 2011. "Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model," Statistical Papers, Springer, vol. 52(2), pages 455-467, May.
    4. Lemonte, Artur J. & Cordeiro, Gauss M., 2009. "Birnbaum-Saunders nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4441-4452, October.
    5. Barreto-Souza, Wagner & Vasconcellos, Klaus L.P., 2011. "Bias and skewness in a general extreme-value regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1379-1393, March.
    6. Koenker, Roger & Yoon, Jungmo, 2009. "Parametric links for binary choice models: A Fisherian-Bayesian colloquy," Journal of Econometrics, Elsevier, vol. 152(2), pages 120-130, October.
    7. Chu-Ping C. Vijverberg & Wim P. M. Vijverberg, 2016. "Pregibit: a family of binary choice models," Empirical Economics, Springer, vol. 50(3), pages 901-932, May.
    8. Brathwaite, Timothy & Walker, Joan L., 2018. "Asymmetric, closed-form, finite-parameter models of multinomial choice," Journal of choice modelling, Elsevier, vol. 29(C), pages 78-112.
    9. Chénangnon Frédéric Tovissodé & Aliou Diop & Romain Glèlè Kakaï, 2021. "Inference in skew generalized t-link models for clustered binary outcome via a parameter-expanded EM algorithm," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-31, April.
    10. Anika Reichert & Rowena Jacobs, 2018. "The impact of waiting time on patient outcomes: Evidence from early intervention in psychosis services in England," Health Economics, John Wiley & Sons, Ltd., vol. 27(11), pages 1772-1787, November.
    11. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    12. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    13. Fosgerau, Mogens & Bierlaire, Michel, 2007. "A practical test for the choice of mixing distribution in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 784-794, August.
    14. Lanot, Gauthier & Walker, Ian, 1998. "The union/non-union wage differential: An application of semi-parametric methods," Journal of Econometrics, Elsevier, vol. 84(2), pages 327-349, June.
    15. Fabio M. Manenti & Stefano Comino & Marialaura Parisi, 2005. "From Planning to Mature: on the Determinants of Open Source Take-Off," Industrial Organization 0507006, University Library of Munich, Germany, revised 29 Sep 2005.
    16. Töpfer, Marina, 2017. "Detailed RIF decomposition with selection: The gender pay gap in Italy," Hohenheim Discussion Papers in Business, Economics and Social Sciences 26-2017, University of Hohenheim, Faculty of Business, Economics and Social Sciences.
    17. Norma B. Coe & Jing Guo & R. Tamara Konetzka & Courtney Harold Van Houtven, 2019. "What is the marginal benefit of payment‐induced family care? Impact on Medicaid spending and health of care recipients," Health Economics, John Wiley & Sons, Ltd., vol. 28(5), pages 678-692, May.
    18. Bucher, Axel & El Ghouch, Anouar & Van Keilegom, Ingrid, 2014. "Single-index quantile regression models for censored data," LIDAM Discussion Papers ISBA 2014001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Klein, Roger & Vella, Francis, 2010. "Estimating a class of triangular simultaneous equations models without exclusion restrictions," Journal of Econometrics, Elsevier, vol. 154(2), pages 154-164, February.
    20. Park, Byeong U. & Simar, Léopold & Zelenyuk, Valentin, 2017. "Nonparametric estimation of dynamic discrete choice models for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 97-120.

    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:sankhb:v:82:y:2020:i:1:d:10.1007_s13571-018-0179-9. 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.