Bayesian Statistical Inference For Quantile Ragression Model With Nonignorable Missing Data

Missing data is often appear in the phenomenon,such as biological genetics,educational psychology,social science,economics and other fields.In the past,most of the researches are carried out under the background of random missing,some missing data is related to themselves,so it is necessary to study nonignorable missing data.The quantile regression model is an extension of the linear regression model.It is widely used inference,social science,econometrics,survival analysis,microanalytic and so on.The quantile regression model does not need to make any assumptions about random errors.The quantile regression model which is not sensitive to the existence of outliers has few constraints,good stability,and will not be affected by heterosexuality.So,it makes up for the deficiency of least square regression.This paper discussed the bayesian parameter estimation and model selection of quantile regression model with nonignorable missing response variables.In order to better discuss bayesian statistical inference with nonignorable response variables,we assumed that the random error term obeys the asymmetric Laplace distribution,and used the mixed representation method of exponential distribution and normal distribution to represent the asymmetric Laplace distribution.In addition,because the response variables cannot be ignored,we used logistic regression model to describe the mechanism of missing data and imputed the missing part of response variables.The Bayesian estimation of unknown parameters are given.But due to the posterior distribution density function in the form of a more complex and has a high dimensional integral,so we use Gibbs sampling methods and Metropolis-Hastings sampling algorithm to sampling the parameters.At last,a simulation study and a real data example are used to verify the effectiveness of our methods.