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Bias correction for a class of multivariate nonlinear regression models

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  • Cordeiro, Gauss M.
  • Vasconcellos, Klaus L. P.

Abstract

In this paper, we derive general formulae for second-order biases of maximum likelihood estimates which can be applied to a wide class of multivariate nonlinear regression models. The class of models we consider is very rich and includes a number of commonly used models in econometrics and statistics as special cases, such as the univariate nonlinear model and the multivariate linear model. Our formulae are easy to compute and give bias-corrected maximum likelihood estimates to order n-1, where n is the sample size, by means of supplementary weighted linear regressions. They are also simple enough to be used algebraically in order to obtain closed-form expressions in special cases.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:35:y:1997:i:2:p:155-164
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    References listed on IDEAS

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    1. Gallant, A. Ronald, 1975. "Seemingly unrelated nonlinear regressions," Journal of Econometrics, Elsevier, vol. 3(1), pages 35-50, February.
    2. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
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    Cited by:

    1. 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.
    2. Di Caterina, Claudia & Kosmidis, Ioannis, 2019. "Location-adjusted Wald statistics for scalar parameters," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 126-142.
    3. 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.
    4. 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.
    5. Ospina, Raydonal & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2006. "Improved point and interval estimation for a beta regression model," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 960-981, November.
    6. Zhang, Rui & Shonkwiler, J. Scott, 2017. "Bias Correction of Welfare measures in Non-Market Valuation: Comparison of the Delta Method, Jackknife and Bootstrap," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258099, Agricultural and Applied Economics Association.
    7. 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.
    8. Gauss Cordeiro & Lúcia Barroso, 2007. "A third-order bias corrected estimate in generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 76-89, May.
    9. 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.

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