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Title: On consistency and inference for Bayesian quantile regression based on the asymmetric Laplace density Authors:  Karthik Sriram - Indian Institute of Management India (India) [presenting]
Abstract: The `misspecified' asymmetric Laplace density (ALD) is used as a working likelihood for Bayesian quantile regression (BQR). It has been previously shown posterior consistency for the true quantile regression parameters under this misspecification. It was further argued square-root-n consistency. In a recent correction note, it has been pointed out that the argument for square-root-n-rate was incorrect, but could not resolve the issue. We first show that square-root-n consistency can be achieved under some additional regularity conditions. We then discuss its connection to posterior inference with some potential extensions. In particular, we compare two previous works, both of which proposed an approach for posterior inference with BQR based on ALD.