Open Access
June 2012 Spatial Quantile Multiple Regression Using the Asymmetric Laplace Process
Kristian Lum, Alan E. Gelfand
Bayesian Anal. 7(2): 235-258 (June 2012). DOI: 10.1214/12-BA708


We consider quantile multiple regression through conditional quantile models, i.e. each quantile is modeled separately. We work in the context of spatially referenced data and extend the asymmetric Laplace model for quantile regression to a spatial process, the asymmetric Laplace process (ALP) for quantile regression with spatially dependent errors. By taking advantage of a convenient conditionally Gaussian representation of the asymmetric Laplace distribution, we are able to straightforwardly incorporate spatial dependence in this process. We develop the properties of this process under several specifications, each of which induces different smoothness and covariance behavior at the extreme quantiles.

We demonstrate the advantages that may be gained by incorporating spatial dependence into this conditional quantile model by applying it to a data set of log selling prices of homes in Baton Rouge, LA, given characteristics of each house. We also introduce the asymmetric Laplace predictive process (ALPP) which accommodates large data sets, and apply it to a data set of birth weights given maternal covariates for several thousand births in North Carolina in 2000. By modeling the spatial structure in the data, we are able to show, using a check loss function, improved performance on each of the data sets for each of the quantiles at which the model was fit.


Download Citation

Kristian Lum. Alan E. Gelfand. "Spatial Quantile Multiple Regression Using the Asymmetric Laplace Process." Bayesian Anal. 7 (2) 235 - 258, June 2012.


Published: June 2012
First available in Project Euclid: 16 June 2012

zbMATH: 1330.62197
MathSciNet: MR2934947
Digital Object Identifier: 10.1214/12-BA708

Keywords: conditional quantiles , MCMC , Quantile regression , spatial statistics

Rights: Copyright © 2012 International Society for Bayesian Analysis

Vol.7 • No. 2 • June 2012
Back to Top