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 ...

Quantile regression is an important tool in data analysis. Linear regression, or more generally, parametric quantile imposes often too restrictive assumptions. Nonparametric avoids making distributional assumptions, but might have the disadvantage of not exploiting modelling elements that be brought in. A semiparametric approach towards estimating conditional curves proposed. It based on a rece...

The dissertation consists of two distinct but related research projects. First of all, we study the Bayesian analysis on the two-piece location-scale models, which contain several well-known subdistributions, such as the asymmetric Laplace distribution, the -skew normal distribution, and the skewed Student-t distribution. The use of two-piece location-scale models is an attractive method to mod...

The finite sample theory using higher order asymptotics provides better approximations of the bias and mean squared error (MSE) for a class of estimators. However, no finite sample theory result is available for the quantile regression and the literature on the quantile regression has been entirely on the first-order asymptotic theory. This paper develops new analytical results on the second-or...

We consider nonlinear quantile regression involving multilayer perceptrons (MLP). In this paper we investigate the asymptotic behavior of quantile regression in a general framework. First by allowing possibly non-identifiable regression models like MLP's with redundant hidden units, then by relaxing the conditions on the density of the noise. In this paper, we present an universal bound for the...

Ordinary linear and generalized linear regression models relate the mean of a response variable to a linear combination of covariate effects and, as a consequence, focus on average properties of the response. Analyzing childhood malnutrition in developing or transition countries based on such a regression model implies that the estimated effects describe the average nutritional status. However,...

Gradient based optimization methods often converge quickly to a local optimum. However, the check loss function used by quantile regression model is not everywhere differentiable, which prevents the gradient based optimization methods from being applicable. As such, this paper introduces a smooth function to approximate the check loss function so that the gradient based optimization methods cou...

We use quantile regressions to estimate whether the relation between school quality and performance on standardized tests differs at different points in the conditional distribution of ‘test score gains’. Previous work has focused only on average school quality effects.  1998 Elsevier Science S.A.

We consider a random effects quantile regression analysis of clustered data and propose a semiparametric approach using empirical likelihood. The random regression coefficients are assumed independent with a common mean, following parametrically specified distributions. The common mean corresponds to the population-average effects of explanatory variables on the conditional quantile of interest...