Some Proposals for Transformation-Based Prediction of Conditional Quantiles When the Outcome Is Bounded

• Activity Number: 180
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Marco Geraci* and M.C. Jones
• Companies: University of South Carolina and The Open University
• Keywords: Aranda-Ordaz transformation ; Box-Cox transformation ; bounded response ; two-stage estimation

Abstract

Inference on conditional quantiles of an outcome variable that is defined on the half line or the unit interval requires appropriate modelling approaches to constrain prediction within the limits of the support. The Box-Cox and, more recently, the Aranda-Ordaz transformation families have been proposed for the estimation of nonlinear quantile functions of, respectively, singly and doubly bounded continuous outcomes. However, Box-Cox and Aranda-Ordaz transformations suffer from a drawback. Back-transformation may be hindered as they do not, in general, have range the entire real line. As a consequence, there is a considerable risk of quantile estimates outside the support of the response over some part of the range of covariate values of interest. Thus, observations for which the objective function is not well-defined need to be excluded and information is lost. To overcome such limitation, alternative transformations are proposed. A simulation study is carried out to assess performance of different models. Alternative quantile estimators are considered, including two-stage, residual cusum process and non-smooth estimators. Some applications are illustrated.