Empirical Likelihood For Tobit Quantileregression Model

As a common data type in survival analysis,censored data has attracted the attention of many statisticians.If the survival time of an individual can not be observed exactly,but only knows that it is less than a certain time point,then the data we get may be left censored data.Tobit quantile regression model provides an effective method to deal with left censored data.LAD estimation is a common method for parameter estimation based on this model.It is difficult to get Wald type confidence interval when LAD is used to estimate unknown parameters.The advantage of the empirical likelihood method is that it can avoid the variance estimation and get the effective confidence interval.Therefore,in this paper,empirical likelihood method is introduced into Tobit quantile regression model under left censored data.The article is divided into the following four parts.In the first part of this paper,empirical likelihood inference in Tobit quantile regression model is studied.Firstly,the estimating function for Tobit quantile regression model is constructed based on left censored data.Then the asymptotical distribution of unknown parameters is proved by empirical likelihood method,and the confidence interval of parameters is obtained.In this part,we also consider the longitudinal data with left censored data.In this data type,we use Tobit quantile regression model to infer the empirical likelihood,so as to obtain the confidence interval.In the simulation study,the models are fitted based on two data types,which verifies the effectiveness of the method.Finally,an actual data in AER package is applied to analyze an example.In the second part of this paper,we mainly study the Bayesian empirical likelihood problem under the censored median regression model.Firstly,based on the objective function proposed by predecessors,the empirical likelihood function is constructed.Then,by giving the prior distribution of unknown parameters,the asymptotic distribution of the posterior distribution is given.Finally,the unknown parameters are estimated by MH algorithm.The simulation experiments show that this method is superior to the empirical likelihood method.The third part of the paper mainly studies the performance of variable selection method in longitudinal data.Firstly,a penalty logarithm conditional likelihood function is proposed based on the conditional density model of random effects.Then the consistency of variable selection and Oracle property are proved.Then the algorithm is designed based on LASSO,ALASSO and SCAD penalty.The numerical results show the finite sample properties of the proposed method and some existing methods.Finally,it is verified by the instance data.The fourth part of the paper is mainly based on the data of per capita cash consumption expenditure of urban residents.Because the data is stored in the form of panel data,the conditional density model of panel data is established firstly,and then the variables are selected.At the same time,the effectiveness of the variable selection method in the conditional density model of random effects of panel data is verified by simulation experiments.