Improved estimators in beta prime regression models

TL;DR

This paper introduces bias correction methods for maximum-likelihood estimators in beta prime regression models, improving estimation accuracy for positive, skewed data with long tails, using analytical and bootstrap techniques.

Contribution

It proposes new bias correction strategies for beta prime regression model estimators, including analytical and bootstrap methods, enhancing estimation accuracy.

Findings

Bias correction yields nearly unbiased estimates.

Bootstrap correction performs well in simulations.

Real data example demonstrates practical effectiveness.

Abstract

In this paper, we consider the beta prime regression model recently proposed by \cite{bour18}, 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.