Abstract:
We consider a power transformation towards a linear quantile regression model. Like the classical Box-Cox transformation, this approach extends the applicability of linear models without resorting to nonparametric smoothing, yet transformations on the quantile models are more natural due to the equivariance property of the quantiles under monotone transformations. We propose an estimation procedure and establish its consistency and asymptotic normality under regularity conditions. The objective function employed in the estimation can also be used to check inadequacy of a power-transformed linear quantile regression model and to obtain inference on the transformation parameter. The proposed approach is shown to be valuable through illustrative examples. The talk is based on joint work with Yunming Mu at the Texas A&M University.