Improved estimators in beta prime regression models

Abstract

In this paper, we consider the beta prime regression model recently proposed in the literature, which is tailored to situations where the response is continuous and restricted to the positive real line with skewed and long tails and the regression structure involves regressors and unknown parameters. We consider two different strategies of bias correction of the maximum-likelihood estimators for the parameters that index the model. In particular, we discuss bias-corrected estimators for the mean and the dispersion parameters of the model. Furthermore, as an alternative to the two analytically bias-corrected estimators discussed, we consider a bias correction mechanism based on the parametric bootstrap. The numerical results show that the bias correction scheme yields nearly unbiased estimates. An example with real data is presented and discussed.

Keywords:

• Beta prime distribution
• Bias correction
• Bootstrap
• Dispersion covariates
• Maximum-likelihood

Notes

1 The function gamlss is implemented in a package in R language (R Core Team 2017) of the same name. In particular, to adjust the BP regression models, we use the glmBP package that applies the gamlss function for this purpose.

2 https://github.com/sesiommedeiros/BiasBPR