Quantile Regression For Complex Data And Its Application

In the fields of economics,biomedical and so on,complex data and causal inference are two important research directions.Furthermore,quantile regression can provide a complete picture of the interested response,and is robust to outliers and heavytailed responses.Therefore,more and more researchers are concerned with quantile treatment effect in causal inference.This thesis mainly focuses on quantile regression or quantile treatment effect of complex data,in which complex data refers to incomplete data such as censored and missing data.The main resluts of this thesis are as follows:(1)Censored quantile regression based on multiply robust propensity scores.One class of methods for dealing with censored quantile regression is based on an informative subset of sample,selected via the propensity score.Propensity score can either be estimated using parametric methods,which poses the risk of misspecification,or obtained using nonparametric approaches,which suffers from ‘curse of dimensionality’.In this study,we propose a new estimation method based on multiply robust propensity score for censored quantile regression,which only requires one of the multiple candidate models for propensity score to be correctly specified,then the resulting estimator is consistent and asymptotic normality,and its asymptotic properties are not affected by propensity score estimators.Extensive simulation studies and a real data analysis on the human immunodeficiency viruses(HIV)are conducted to investigate the good finite sample performance of the proposed estimator.(2)Multiply robust estimation of quantile treatment effects with missing outcomes.There are two types of missing data in causal inference: one is missing counterfactual outcome? the other is missing experimental data caused by other factors.In this study,we develop two multiply robust estimators to deal with the double missing problem.The first one is utilizing the inverse probability weighting approach to develop an objective function based on multiply robust estimations of propensity score and the probability of being observed.The second one is based on augmented inverse probability weighting method,which further relaxes the restriction on the correct specification of outcome regression model.Consistency and asymptotic normality properties of the proposed estimators are investigated.Simulation studies and an empirical analysis of CHARLS dataset are conducted to evaluate the finite sample performance of the proposed method.(3)Estimation of conditional extreme quantile treatment effect for heavy tailed distributions.Extreme events are rare but have significant consequences.In this thesis,assuming that the outcome is heavy-tailed and the conditional quantiles is linear in the covariates at tail quantiles,we first estimate the conditional intermediate quantiles of both the treatment group and control group using the inverse probability weighted method,and then extrapolate these estimators to the high tails.Due to the importance of the extreme value index in the extrapolation method,we develop three Hill-type estimators for the extreme value index,which provides more protections for its accuracy.We present a comprehensive study of the theoretical properties,including the consistency and asymptotic normality of the proposed estimators of the conditional extreme quantile treatment effect and the extreme value index.Simulation studies and an analysis of the low infant birth weight are conducted to investigate the good finite sample performance of the proposed estimator.The main innovations of this thesis are as follows:(1)This paper applies multiple robust estimation to different backgrounds.The first application is to select information subsets with multiply robust propensity scores in censored quantile regression.The second application is to propose two kinds of multiply robust estimates in the quantile treatment effect with missing outcomes.The third application is to estimate the conditional intermediate quantile under heavy-tailed distribution based on multiply robust propensity scores.On the one hand,multiply robust estimation is more robust than parametric method in model misspecification,on the other hand,it can overcome the”curse of dimensionality” brought by nonparametric method.(2)This paper proposes two multiply robust methods to deal simultaneously with the missing counterfactual outcome and the missing experimental data caused by other factors.(3)This paper provides the extrapolation estimation of extreme conditional quantile treatment effect and three extreme value index estimates.Researchers in the fields of economics and biomedicine often pay attention to the extreme quantile treatment effect,but there are few studies in this fields.