Abstract: In this paper,the Bayesian empirical likelihood method is extended to the compound quantile regression model. Firstly,the empirical likelihood function of the compound quantile regression model is constructed, and the conditional posterior distribution of unknown parameters is derived after the prior information is given. Secondly, considering that the posterior distribution of unknown parameters is complex and has implicit equation constraints,a Metropolis-Hastings algorithm with constraints is constructed for point estimation,confidence interval estimation and parameter hypothesis testing of model parameters. The computer simulation results show that when the stochastic error of the model is a thick tail distribution,the Bayesian empirical likelihood compound quantile regression method proposed in this paper has more obvious advantages than the compound quantile regression method,the quantile regression method and the least square method in estimating deviation and variance. Especially when the data contains more anomalies,the proposed method is the most robust. Finally,the paper uses the new method to model and analyze the data of a medical expenditure influencing factor,and finds that compared with other estimation methods,the coefficient obtained by Bayes empirical likelihood compound quantile regression method changes the least before and after estimation,regardless of whether the abnormal points in the data are deleted or not. This provides useful assistance in reducing the impact of unknown outtiers in the date on the model during a real modeling process.

Key words: compound quantile regression, Bayesian empirical likelihood, Metropolis-Hastings algorithm, Bayes factor