Bias-Corrected Maximum Likelihood Estimators in Nonlinear Heteroscedastic Models |
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Authors: | Gauss M. Cordeiro Audrey H. M. A. Cysneiros |
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Affiliation: | 1. Departamento de Estatística e Informática , Universidade Federal Rural de Pernambuco , Recife, Brazil;2. Departamento de Estatística , Universidade Federal de Pernambuco , Recife, Brazil |
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Abstract: | Nonlinear heteroscedastic models are widely used in econometrics and statistical applications. We derive matrix formulae for the second-order biases of the maximum likelihood estimators of the parameters in the mean and variance response which generalize previous results by Cook et al. (1986 Cook , D. R. , Tsai , C. L. , Wei , B. C. ( 1986 ). Bias in nonlinear regression . Biometrika 73 : 615 – 623 .[Crossref], [Web of Science ®] , [Google Scholar]) and Cordeiro (1993 Cordeiro , G. M. ( 1993 ). Bartlett corrections and bias correction for two heteroscedastic regression models . Commun. Statist. Theor. Meth. 22 : 169 – 188 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The biases of the estimators are easily obtained as vectors of regression coefficients from suitable weighted linear regressions. The practical use of such biases is illustrated in a simulation study and in an application to a real data set. |
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Keywords: | Bias correction Cumulant Heteroscedastic model Information matrix Maximum likelihood Method of scoring Nonlinear model |
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