Simultaneous Bayesian Estimation of Multiple Quantiles with an Extension to Hierarchical Models

41 Pages Posted: 27 Jul 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: April 27, 2012

Abstract

Simultaneously modeling multiple quantiles by possibly incorporating constraints across quantiles, in particular that of monotonicity, has been an important problem. While recent attempts to address this problem focus mostly on the monotonicity issue, we take a different route using a Bayesian approach. We propose a parametric pseudo-likelihood based approach for simultaneous Bayesian estimation of multiple quantiles that is computationally simple and has the flexibility to accomodate linear as well as nonlinear model forms along with different types of prior specifications. A unique feature of our method compared to existing approaches is the posterior consistency property for the case of linear quantile regression. Further, we develop a useful extension of our method to a hierarchical setting which is applicable in particular to the normal random effects model and binary regression. We demonstrate our methods using simulations and two real life examples. The first example demonstrates an alternative way to address heteroskedasticity issues in modeling worker’s compensation claims. The second example provides a novel approach to flexibly model inefficiencies of firms in a stochastic frontier analysis applied to a dataset on hospital costs.

Keywords: Asymmetric Laplace distribution, Bayesian quantile regression, Crossing

Suggested Citation

Sriram, Karthik and Ramamoorthi, R. and Ghosh, Pulak, Simultaneous Bayesian Estimation of Multiple Quantiles with an Extension to Hierarchical Models (April 27, 2012). IIM Bangalore Research Paper No. 359. Available at SSRN: https://ssrn.com/abstract=2117722 or http://dx.doi.org/10.2139/ssrn.2117722

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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