Skewness of Maximum Likelihood Estimators in Beta Regression Model

• Activity Number: 421
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Tiago Magalhaes*+ and Denise Botter and Monica Sandoval
• Companies: University of Sao Paulo and University of Sao Paulo and University of Sao Paulo
• Keywords: Beta regression model ; maximum likelihood estimation ; asymptotic skewness

Abstract

The beta regression model can be used to model rates or proportions. We obtain a simple matrix formula of order $n^{-1/2}$, where $n$ is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators of the parameters in beta regression models. The formula is suitable for computer implementation since it involves only simple operations on matrices and vectors. We conduct a simulation study to avaliate the obtained skewness coefficient and apply this expression to real data.