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Corrected maximum-likelihood estimation in a class of symmetric nonlinear regression models

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  • Cordeiro, Gauss M.
  • Ferrari, Silvia L. P.
  • Uribe-Opazo, Miguel A.
  • Vasconcellos, Klaus L. P.

Abstract

In this paper we derive general formulae for second-order biases of maximum-likelihood estimates in a class of symmetric nonlinear regression models. This class of models is commonly used for the analysis of data containing extreme or outlying observations in samples from a supposedly normal distribution. The formulae of the biases can be computed by means of an ordinary linear regression. They generalize some previous results by Cook et al., Biometrika 73 (1986) 615-623, Cordeiro and Vasconcellos, Statist. Probab. Lett. 35 (1997) 155-164 and Cordeiro et al., J. Statist. Comput. Simulation 60 (1998) 363-378. We derive simple closed-form expressions for these biases in special models. Simulation results are presented assessing the performance of the bias corrected estimates which indicate that they have smaller biases than the corresponding unadjusted estimates.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:4:p:317-328
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    References listed on IDEAS

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    2. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
    3. 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.
    4. Berkane, Maia & Bentler, P. M., 1986. "Moments of elliptically distributed random variates," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 333-335, October.
    5. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Citations

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    Cited by:

    1. Vanegas, Luis Hernando & Cysneiros, Francisco José A., 2010. "Assessment of diagnostic procedures in symmetrical nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1002-1016, April.
    2. Galea, Manuel & Paula, Gilberto A. & Cysneiros, Francisco José A., 2005. "On diagnostics in symmetrical nonlinear models," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 459-467, July.
    3. Chun-Zheng Cao & Jin-Guan Lin & Li-Xing Zhu, 2010. "Heteroscedasticity and/or autocorrelation diagnostics in nonlinear models with AR(1) and symmetrical errors," Statistical Papers, Springer, vol. 51(4), pages 813-836, 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. Vicente Cancho & Víctor Lachos & Edwin Ortega, 2010. "A nonlinear regression model with skew-normal errors," Statistical Papers, Springer, vol. 51(3), pages 547-558, September.
    6. 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.
    7. 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.
    8. Lemonte, Artur J. & Cordeiro, Gauss M., 2009. "Birnbaum-Saunders nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4441-4452, October.
    9. Cysneiros, Francisco José A. & Vanegas, Luis Hernando, 2008. "Residuals and their statistical properties in symmetrical nonlinear models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3269-3273, December.

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