On a heavy-tailed parametric quantile regression model for limited range response variables

On the basis of a two-parameter heavy-tailed distribution, we introduce a novel parametric quantile regression model for limited range response variables, which can be very useful in modeling bounded response variables at different levels (quantiles) in the presence of atypical observations. We consider a frequentist approach to perform inferences, and the maximum likelihood method is employed to estimate the model parameters. We also propose a residual analysis to assess departures from model assumptions. Additionally, the local influence method is discussed, and the normal curvature for studying local influence on the maximum likelihood estimates is derived under a specific perturbation scheme. An application to real data is presented to show the usefulness of the new parametric quantile regression model in practice.