Opuscula Math. 32, no. 4 (2012), 761-774
http://dx.doi.org/10.7494/OpMath.2012.32.4.761
Opuscula Mathematica
On the maximum likelihood estimator in the generalized beta regression model
Jerzy P. Rydlewski
Dominik Mielczarek
Abstract. The subject of this article is to present the beta - regression model, where we assume that one parameter in the model is described as a combination of algebraically independent continuous functions. The proposed beta model is useful when the dependent variable is continuous and restricted to the bounded interval. The parameters are obtained by maximum likelihood estimation. We prove that estimators are consistent and asymptotically normal.
Keywords: nonlinear regression, beta distribution, scale parameter, shape parameter, maximum likelihood estimator.
Mathematics Subject Classification: 62J02, 62F10.
- Jerzy P. Rydlewski
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
- Dominik Mielczarek
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
- Received: 2011-06-11.
- Revised: 2012-02-25.
- Accepted: 2012-09-26.
