处理效应差异中位数的有效估计

Drawing differences about the effects of treatments and actions is a common challenge in econometrics, epidemiology and other fields. In the existed papers, nonparametric methods be used to estimate the propensity scores or the regression models respectively or meanwhile, then the the estimators of the treatment effects difference can be constructed. On some specific conditions, these estimators enjoy good property in theory, however, the numeric performance of the proposed estimators be not given. It is well known the curse of dimensionality exists when the nonparametric methods be used for these estimators. So in current studies, the parametric hypotheses of the propensity scores or the regression models be used to estimate the treatment effects difference. Although these estimators have good performance in simulations, the optimal theory can not be achieved. Treatment effects be usually assessed by the mean difference or the median difference. The latter is much robust than the former, however, for the complexity the study of the median difference is less than that of the mean difference. In this project, under general conditions, an efficient estimator with good performance in simulations and the optimal theory property will be constructed. Then the proposed estimator can be used to assess treatment effects difference well in many fields.

在经济学、遗传病学等很多领域中，处理效应差异的研究极具挑战性。在已有的处理效应差异的工作中，非参数方法用来对分组机制或回归模型分别进行估计或同时估计，然后构造处理效应差异的估计。在一定的条件下估计具有良好的理论性质，但是不切合实际也未经过数值模拟验证。鉴于之前的研究中非参数方法会遇到维数祸根的问题，后续的研究基于对分组机制和回归模型进行参数模型假设去估计处理效应差异，这些研究角度不同，数值模拟结果可以进行比较，但理论没有可比性，同时这些估计也没有达到理论上最优的结果。平均处理效应差异和处理效应差异中位数经常用来评估处理效应差异。处理效应差异中位数较平均处理效应更稳健，然而研究更复杂因而相关的研究甚少。该项目将在更一般的条件下构造出处理效应差异中位数的有效估计，这样的估计具有最优的理论性质，并且数值模拟结果良好，使得在医学等应用中能更好地评估处理效应差异。