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Bayesian quantile regression

Cemmap Working Paper CWP05/06

Recent work by Schennach (2005) has opened the way to a Bayesian treatment of quantile regression. Her method, called Bayesian exponentially tilted empirical likelihood (BETEL), provides a likelihood for data y subject only to a set of m moment conditions of the form Eg(y, θ) = 0 where θ is a k dimensional parameter of interest and k may be smaller, equal to or larger than m. The method may be thought of as construction of a likelihood supported on the n data points that is minimally informative, in the sense of maximum entropy, subject to the moment conditions.

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