Statistical Inference On Quantile Autoregression Models With Nonignorable Missing Data

Missing data has always been a hot issue in statistical research.At present,most domestic and foreign studies assume that the missing data mechanism is ignorable.However,in many practical applications,people often encounter situations where the missing data mechanism cannot be ignored.At this time,if we still use the method of dealing with ignore missing data to study such missing data,it may lead to biased estimates or even wrong conclusions.At the same time,in the traditional time series data analysis,the autoregressive model under normal assumptions has limitations in dealing with heteroscedastic data such as peaks and thick tails,while the quantile autoregression model does not require strong assumptions.It is not affected by outliers and is more robust than traditional estimates.This paper discusses empirical likelihood estimation and Bayesian estimation of model parameters for quantile autoregression models with nonignorable missing data.Its main contents include:(1)For time series data that contains nonignorable missing data and spikes or thick tails in the data,limitations of traditional model estimation,etc.,establish a quantile autoregression model with nonignorable missing data;(2)For the mechanism of missing data that cannot be ignored,establish a Logistic regression model,and discuss the estimation of model parameters based on the empirical likelihood method;(3)For the regression coefficients in the model,the regression parameter estimation equation based on the inverse probability weighted interpolation method is established,and the problem of estimating the regression parameters in the estimation equation is discussed based on the empirical likelihood method;(4)Establish a Bayesian quantile autoregression model with nonignorable missing data,and deduce the posterior distribution of parameters by discussing the prior distribution of model parameters,and discuss the model parameter estimation problem based on MCMC method;(5)Through simulation research,verify that the estimation methods proposed in this paper is consistent.Compared with the CC method and the estimation of the entire data set,the results are: in the case of large samples,the estimates using the inverse probability weighted empirical likelihood method and the Bayesian method are close to the entire data set,and are better than the CC method.