Posterior Consistency of Bayesian Quantile Regression Under a Mis-Specified Likelihood Based on Asymmetric Laplace Density

29 Pages Posted: 6 Aug 2012

See all articles by Karthik Sriram

Karthik Sriram

Indian Institute of Management (IIMB), Bangalore

R. Ramamoorthi

Michigan State University

Pulak Ghosh

Indian Institute of Management (IIMB), Bangalore

Date Written: May 30, 2011

Abstract

We provide a theoretical justification for the widely used and yet only empirically verified approach of using Asymmetric Laplace Density(ALD) in Bayesian Quantile Regression. We derive sufficient conditions for posterior consistency of the quantile regression parameters even if the true underlying likelihood is not ALD, by considering both the case of random as well as non-random covariates. While existing literature on misspecified models address more general models, our approach of exploiting the specific form of ALD allows for a more direct derivation. We verify that the conditions so derived are satisfied by a wide range of potential true underlying probability distributions. We also show that posterior consistency holds even in the case of improper priors as long as the posterior is well defined. We demonstrate the working of the method using simulations.

Keywords: consistency, asymmetric laplace density, Kullback-Leibler divergence, quantile regression, posterior distribution

Suggested Citation

Sriram, Karthik and Ramamoorthi, R. and Ghosh, Pulak, Posterior Consistency of Bayesian Quantile Regression Under a Mis-Specified Likelihood Based on Asymmetric Laplace Density (May 30, 2011). IIM Bangalore Research Paper No. 340. Available at SSRN: https://ssrn.com/abstract=2123083 or http://dx.doi.org/10.2139/ssrn.2123083

Karthik Sriram (Contact Author)

Indian Institute of Management (IIMB), Bangalore ( email )

Bannerghatta Road
Bangalore, Karnataka 560076
India

R. Ramamoorthi

Michigan State University ( email )

Agriculture Hall
East Lansing, MI 48824-1122
United States

Pulak Ghosh

Indian Institute of Management (IIMB), Bangalore ( email )

Bannerghatta Road
Bangalore, Karnataka 560076
India

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