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Abstract:
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Quantile regression provides information about the conditional quantiles of the data. However, the quantile crossing problem arises when each quantile curves are estimated individually. Especially this problem is exacerbated in the context of Bayesian inference since it not only invalidates the estimated quantile curves but also their uncertainty information. Recently, it has been shown that Bayesian quantile regression model based on asymmetric Laplace likelihood does not lead to asymptotically valid posterior inference so that suitable likelihood correction for the covariance matrix is necessary. We extend this likelihood correction method to the joint quantile estimation problem and suggest using a constrained prior under this approximate likelihood to ensure non-crossing of the estimated quantile curves. We compare the simulation results with other quantile regression methods in terms of coverage probability and posterior inference on the quantile curves.
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