Improved estimators for generalized linear models with dispersion covariates
- 1 December 1998
- journal article
- research article
- Published by Informa UK Limited in Journal of Statistical Computation and Simulation
- Vol. 62 (1), 91-104
- https://doi.org/10.1080/00949659808811926
Abstract
This paper addresses the issue of bias reduction of maximum likelihood estimators in generalized linear models with dispersion covariates. For this class of models, we derive general formulae for the second-order biases of maximum likelihood estimators of the linear and dispersion parameters, linear predictors, precision parameters and mean values. Our formulae cover many important and commonly used models and can be viewed as an extension of the results in Cordeiro and McCullagh (1991) and Cordeiro (1993)These formulae are easily implemented by means of supplementary weighted linear regressions. They are also simple enough to be used algebraically to obtain several closed-form expressions in special models. The practical use of such bias corrections is illustrated in a simulation study.Keywords
This publication has 11 references indexed in Scilit:
- Bias correction for a class of multivariate nonlinear regression modelsStatistics & Probability Letters, 1997
- Bias correction in ARMA modelsStatistics & Probability Letters, 1994
- Bias correction for exponential family nonlinear modlesJournal of Statistical Computation and Simulation, 1992
- Bartlett corrections and bias correction for two heteroscedastic regression modelsCommunications in Statistics - Theory and Methods, 1992
- Generalized Linear ModelsPublished by Springer Science and Business Media LLC ,1989
- Bias in nonlinear regressionBiometrika, 1986
- Review: P. McCullagh, J. A. Nelder, Generalized Linear ModelsThe Annals of Statistics, 1984
- A Note on Bias Correction in Maximum Likelihood Estimation with Logistic DiscriminationTechnometrics, 1980
- Theoretical StatisticsPublished by Springer Science and Business Media LLC ,1974
- Bias and accuracy of parameter estimates in a quantal response modelBiometrika, 1971