Abstract This paper studies the connections among the asymmetric Laplace probability density (ALPD), maximum likelihood, maximum entropy and quantile regression. We show that the maximum likelihood problem is equivalent to the solution of a maximum entropy problem where we impose moment...

In this article, we develop a Bayesian method for quantile regression in the case of dichotomous response data. The frequentist approach to this type of regression has proven problematic in both optimizing the objective function and making inference on the regression parameters. By accepting...

In this paper we will present recent work on a new unit-level small area methodology that can be used with continuous and discrete outcomes. The proposed method is based on constructing a model-based estimator of the distribution function by using a nested-error regression model for the...

Quantile regression provides a convenient framework for analyzing the impact of covariates on the complete conditional distribution of a response variable instead of only the mean. While frequentist treatments of quantile regression are typically completely nonparametric, a Bayesian formulation...

In this paper we will present recent work on a new unit-level small area methodology that can be used with continuous and discrete outcomes. The proposed method is based on constructing a model-based estimator of the distribution function by using a nested-error regression model for the...