Bayesian Quantile Regression And Its Application

Since Koenker and Bassett put forward quantile regression in 1978,quantile regression has become an important method for studying the distribution of dependent variables.It has extended the research on the basis of classical mean regression and complement the limitations of classical regression.The quantile regression does not require mandatory assumptions on the distribution and not only can measure the impact of the independent variable on the distribution center of the dependent variable but also can measure the impact on the tail.It can more comprehensively reflect the information contained in the research question.At the same time,the quantile regression has better robustness and is not affected by outliers.So it is widely used in the fields of economy and finance.As the traditional quantile regression is computationally inefficient in the estimation of parameters,and the fine nature of the quantile regression is difficult to show when the sample size is small.So this paper uses the Bayesian method to do statistical inference based on the traditional quantile regression.This paper consists of four parts.The first part is the introduction,and it mainly introduces the research background and research significance of Bayesian quantile regression.It describes its development history and the current research results in this area at home and abroad,and lists the main research of this paper.The second part mainly introduces the basic theoretical knowledge of traditional quantile regression.It introduces the quantile and loss function,and gives the parameter estimation equation of quantile regression,and briefly introduces the traditional quantile regression algorithm and its advantages and disadvantages.The third chapter systematically expounds the basic principles and estimation methods of Bayesian quantile regression,and introduces the Bayesian quantile regression in the case of continuous dependent variables and discrete dependent variables respectively.The fourth part is the empirical part,based on two cases of continuous dependent variables and discrete dependent variables,studying the comprehensive economic strength of 14 prefecture-level cities in Liaoning Province in 2016 and the credit risk of listed companies respectively.The first empirical result shows that the model can describe the influence of evaluation indicators on the comprehensive economic strength of cities under different quintiles.The result can help governments adjust their economic development strategies in time according to their actual development level,and enhance the overall economic strength and reduce the development gap.The second empirical result shows that the Bayesian quantile regression model can describe the heterogeneity of financial indicators for listed companies under different credit levels,and it also has good effect on default risk prediction.Accuracy,ROC curve and AUC value show that the fitting effect is good.