关键词: 面板数据, 贝叶斯自适应Lasso, 分位数回归, 非对称指数幂分布

Abstract: At present, Bayesian quantile regression is almost implemented on the basis of the asymmetric Laplace distribution (ALD). However, ALD displays medium tails and lacks tail parameters, which make it unsuitable for real data characterized by sharp peaks, thick tails and skewness, resulting in Bayesian quantile estimation deviation. An extension of classical Bayesian adaptive lasso quantile regression method is proposed to overcome these defects using the asymmetric exponential power (AEP) distribution with left and right tail parameters. Using an adaptive Metropolis-Hastings within Gibbs algorithm, it is applied to panel data for the first time. AEP method is compared with Bayesian adaptive lasso quantile regression method based on skew exponential power (SEP) distribution and ALD to check the validity of AEP method. The results show that AEP method is less susceptible to the interference of extreme values and has better robustness than SEP method and ALD method. Furthermore, under different error distributions and quantile levels, AEP method has the function of shrinking parameters with higher precision. Finally, 36 Chinese retail listed companies are selected as the empirical research object, and the influencing factors of stock return rate are effectively screened and estimated with AEP method, which further verifies its ability of variable selection and parameter estimation in practical problems.

Key words: Panel Data, Bayesian Adaptive Lasso, Quantile Regression, Asymmetric Exponential Power Distribution