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- Title
Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood.
- Authors
Yang, Yunwen; Wang, Huixia Judy; He, Xuming
- Abstract
The paper discusses the asymptotic validity of posterior inference of pseudo-Bayesian quantile regression methods with complete or censored data when an asymmetric Laplace likelihood is used. The asymmetric Laplace likelihood has a special place in the Bayesian quantile regression framework because the usual quantile regression estimator can be derived as the maximum likelihood estimator under such a model, and this working likelihood enables highly efficient Markov chain Monte Carlo algorithms for posterior sampling. However, it seems to be under-recognised that the stationary distribution for the resulting posterior does not provide valid posterior inference directly. We demonstrate that a simple adjustment to the covariance matrix of the posterior chain leads to asymptotically valid posterior inference. Our simulation results confirm that the posterior inference, when appropriately adjusted, is an attractive alternative to other asymptotic approximations in quantile regression, especially in the presence of censored data.
- Subjects
QUANTILE regression; BAYESIAN analysis; LAPLACE transformation; MARKOV chain Monte Carlo; COVARIANCE matrices
- Publication
International Statistical Review, 2016, Vol 84, Issue 3, p327
- ISSN
0306-7734
- Publication type
Article
- DOI
10.1111/insr.12114