Estimation of conditional M-quantile treatment effect

Causal effect is an important issue in diverse research fields. When some confounders are given, we then need to study the causal effect in a conditional manner and estimate the relevant unknown quantities such as conditional treatment effect. In this project, we will construct conditional M-quantile treatment effect (CMqTE), which is robust against outliers, to capture the heterogeneity through, say, quantile or expectile sheet, that is a function of quantile levels and given confounders, to examine one more type of heterogeneity in specific subpopulations decided by the confounders. We will then investigate the asymptotic properties of propensity score-based under nonparametric, semiparametric, parametric and true (oracle) regression structure. Through these studies, we can, when the model is correctly specified, then provide the comparisons among the methods in the asymptotic manner and insight into the pros and cons under different model structures. Due to their advantages of alleviating curse of dimensionality and model misspecification, we will pay a particular attention to the semiparametric estimations. Also we investigate properties of these methods when the underlying models are misspecified globally and locally and discuss the bias correction. Numerical studies will also be conducted to examine the finite sample performance of the methods.

This research project will provide insight into the asymptotic efficiency of various estimations such that the results can guide the use of the methods in practice and expect the new theory developed in the course of the project will have a lasting impact in the relevant fields.