Tobit Quantile Regression Research Articles

A Bayesian Nonparametric Approach to Inference for Quantile Regression

We develop a Bayesian method for nonparametric model–based quantile regression. The approach involves flexible Dirichlet process mixture models for the joint distribution of the response and the covariates, with posterior inference for different quantile curves emerging from the conditional response distribution given the covariates. An extension to allow for partially observed responses leads to a novel Tobit quantile regression framework. We use simulated data sets and two data examples from the literature to illustrate the capacity of the model to uncover nonlinearities in quantile regression curves, as well as nonstandard features in the response distribution.

Bayesian analysis of a Tobit quantile regression model

This paper develops a Bayesian framework for Tobit quantile regression. Our approach is organized around a likelihood function that is based on the asymmetric Laplace distribution, a choice that turns out to be natural in this context. We discuss families of prior distributions on the quantile regression vector that lead to proper posterior distributions with finite moments. We show how the posterior distribution can be sampled and summarized by Markov chain Monte Carlo methods. A method for comparing alternative quantile regression models is also developed and illustrated. The techniques are illustrated with both simulated and real data. In particular, in an empirical comparison, our approach out-performed two other common classical estimators.