Bayesian empirical likelihood for quantile regression

By Yunwen Yang, Xuming He. 2012

143 citations recorded by the source corpus.

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful investigation. This paper considers the Bayesian empirical likelihood approach to quantile regression. Taking the empirical likelihood into a Bayesian framework, we show that the resultant posterior from any fixed prior is asymptotically normal; its mean shrinks toward the true parameter values, and its variance approaches that of the maximum empirical likelihood estimator. A more interesting case can be made for the Bayesian empirical likelihood when informative priors are used to explore commonality across quantiles. Regression quantiles that are computed separately at each percentile level tend to be highly variable in the data sparse areas (e.g., high or low percentile levels). Through empirical likelihood, the proposed method enables us to explore various forms of commonality across quantiles for efficiency gains. By using an MCMC algorithm in the computation, we avoid the daunting task of directly maximizing empirical likelihood. The finite sample performance of the proposed method is investigated empirically, where substantial efficiency gains are demonstrated with informative priors on common features across several percentile levels. A theoretical framework of shrinking priors is used in the paper to better understand the power of the proposed method.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e248832b76e5dfd2c48ed196b8b9c5fc3dfec812

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood (2016, methodology): “Lancaster & Jun (2010) considered exponential tilted empirical likelihood, while Otsu (2008) and Yang & He (2012) considered empirical likelihood.”
Bayesian Estimation and Comparison of Moment Condition Models (2016, methodology): “) on θ, moment condition models can in principle be subjected to a Bayesian semiparametric analysis. Applications of this idea are given for instance by Lancaster and Jun (2010), Kim and Yang (2011), Yang and He (2012), Xi et al. (2016) to handle moment condition models, by Rao and Wu (2010) in comp”
Hamiltonian Monte Carlo sampling in Bayesian empirical likelihood computation (2017, methodology): “These include Fang and Mukerjee (2006), Chang and Mukerjee (2008), Grendár and Judge (2009a) and Yang and He (2012).”
Calibrating general posterior credible regions (2015, methodology): “To demonstrate this, we revisit a simulation example presented in Yang and He (2012). For τ = 0.”