Statistical Inference And Application For Rubin Causal Models And Regression Models With Some Types Of Data

Some types of data are often encountered in almost all scientific disciplines,including economics,aerography,biology,epidemiology and sociology,etc.For example,high-dimensional data,multicollinearity data,longitudinal data,heavy tailed data.Regression and causal analyses are the powerful tools to study these data set and show the relations between the response variable,treatment indicator variable and covariates.Based on regression and causal analyses,researchers can explain some results in practices and predict the future development trends,then provide some suggestions for the policy-makers and companies.If we ignore the inherent structures of these data and directly use the simple Rubin causal models and regression models to fit the data and make statistical inferences,then the resulting estimators will lead to the poor prediction accuracies even the invalid methods.Therefore,there are some theoretical meanings and realistic application values to discuss the Rubin causal models and regression models under some types of data,and it is also one of the hot issues in the modern statistical studies.This dissertation mainly considers the estimations and applications for the Rubin causal models and regression models with some types of data,such as highdimensional data,multicollinearity data,longitudinal data.The detailed of five research contents are presented as follows.(1)For the Rubin causal models with multicollinearity in high-dimensional data,we consider the estimation problem of average treatment effect.Firstly,the Elastic-net regression adjustment estimator for the average treatment effect is proposed based on the Elastic-net penalty and regression adjustment method,and the asymptotic properties of the proposed estimator are shown under some regularity conditions.Secondly,Neyman-type conservative estimator for the asymptotic variance is proposed,which yields tighter confidence interval than the unadjusted estimator.Finally,some simulation studies and an analysis for the real dataset of breast cancer patients are carried out to show that the Elastic-net adjusted method is better in addressing collinearity problem than the existing methods.(2)For the Rubin causal models with longitudinal data,we consider the estimation problem of average treatment effect.Firstly,the estimator of propensity score is proposed based on the generalized boosted methods,then the inverse probability weighting estimator of average treatment effect is obtained.Secondly,we use the proposed method to analysis the NGHS data,and study the race effects for the systolic blood pressure,diastolic blood pressure and abnormal blood pressure problems.Finally,some simulation results are conducted to illustrate the effectiveness of the proposed method.(3)For the Rubin causal models with longitudinal data,we consider the estimation problem of quantile treatment effect.Firstly,according to the technique of quantile regression and generalized boosted methods,the estimator of quantile treatment effect is proposed.Secondly,we use the proposed method to analysis the NGHS data,and study the race effects for low-density lipoprotein cholesterol(LDL)and Triglyceride(TG)based on some different quantiles.Finally,we conduct some simulation studies to illustrate the finite sample performance of our proposed method.(4)For the quantile varying-coefficient models with unknown link function,we consider the identification and estimation problems.Firstly,We provide new identification conditions which are weaker than existing ones.Secondly,polynomial splines are used to estimate both the varying coefficients and the link function,then the convergence rate of the estimator is established.Finally,some simulation studies and a real data application are carried out to assess the finite sample performance of the estimators.(5)For the unbalanced Panel data models with errors-in-variables,we consider the problems for parameter estimation and testing problems under restricted condition.Firstly,we give the unknown parameter estimators with or without linear constraints based on the method of bias corrected method,and discuss the asymptotic properties of the proposed estimators under some regularity conditions.Then,to test the validity of linear restriction,a test method is constructed based on the difference of the corrected residual sum of squares under the null and alternative hypotheses,and its limiting distribution is derived.Finally,the effectiveness of the proposed estimation and testing methods are assessed by some simulation studies and one real data analysis.