Abstract: In the mixed-effects models of panel data, it is difficult to estimate the parameters of the model because of a large number of unknown random effects. At the same time, because the distribution of random errors is unknown, the random errors under different distributions increase the complexity of model computation and bring difficulties to the selection and estimation of variables for the coefficients of fixed and random effects. To solve this problem, this paper establishes a double Bayesian Adaptive Lasso quantile regression model, and introduces the Adaptive Lasso penalty function into the panel data with fixed and random effects at the same time. A Gibbs sampling algorithm for parameter estimation is also constructed. The Monte Carlo simulation results show that the method not only accurately estimates the parameter coefficients of different panel data models, but also allows the selection of important variables.

Key words: double adaptive Lasso penalty, Gibbs sampling algorithm, quantile regression, random effects, Bayesian method