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

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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. 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.
    10. 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.
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