Statistical Science) Bayesian Spatial Quantile Regression by Kristian Lum Department of Statistical Science Duke University

Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the upper and lower tails. This paper develops a theory of quantile regression in the tails. Specifically, it obtains the large sample properties of extremal (extr...

This paper is a study of the application of Bayesian Exponentially Tilted Empirical Likelihood to inference about quantile regressions. In the case of simple quantiles we show the exact form for the likelihood implied by this method and compare it with the Bayesian bootstrap and with Jeffreys’ method. For regression quantiles we derive the asymptotic form of the posterior density. We also exami...

An algorithm for computing parametric linear quantile regression estimates subject to linear inequality constraints is described. The algorithm is a variant of the interior point algorithm described in Koenker and Portnoy (1997) for unconstrained quantile regression and is consequently quite efficient even for large problems, particularly when the inherent sparsity of the resulting linear algeb...