A Simple Mean-Parameterized Maxwell Regression Model for Positive Response Variables

Abstract

We study a quite simple parametric regression model that may be very useful to model positive response variables in practice. The frequentist approach is considered to perform inferences, and the traditional maximum likelihood method is employed to estimate the unknown parameters. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. We also derive a closed-form expression for the second-order bias of the maximum likelihood estimator, which is easily computed as an ordinary linear regression and is then used to define bias-corrected maximum likelihood estimates. We consider the normalized quantile residuals for the new parametric regression model to assess departures from model assumptions, and global and local influence methods are also discussed. Applications to real data are considered to illustrate the new regression model in practice, and comparisons with two of the most popular existing regression models are made.