关键词: 可加模型, 惩罚样条, 非参数分位回归, 马尔科夫蒙特卡罗算法

Abstract: In the paper, additive quantile regression models for panel data is discussed in the framework of Bayesian analysis. By using penalty spline of low rank thin plate and introducing dummy variables, the nonparametric models are transformed into parametric ones. Then, under the assumption that random error is subject to asymmetric Laplace distribution, a Bayesian hierarchical quantile regression model is established. At the same time, the conditional posterior distribution of all unknown parameters are introduced and a Gibbs sampling algorithm is also proposed to estimate them. The computer simulation results show that the proposed method is more robust than the classical additive mean regression methods. Finally, taking the consumer expenditure panel data as an example, the new method is demonstrated to study the impact of the income structure of our rural residents on consumption expenditure. Some useful new conclusions have been obtained from the model. The empirical results show that for rural residents, whether its consumption is high, medium or low, the positive stimulus effect of wage income and household business income on consumer expenditure is more obvious. Furthermore, compared with high consumption rural residents, the growth rate of consumption expenditure for low consumption rural residents is slower with the increase of income.

Key words: Additive Model, Penalty Spline, Nonparametric Quantile Regression, Markov Chain Monte Carlo Algorithm