更改

删除3字节 、 2021年6月4日 (五) 00:30
无编辑摘要
第39行: 第39行:  
If we could observe, for each individual, <math>y_{1}(i)</math> and <math>y_{0}(i)</math> among a large representative sample of the population, we could estimate the ATE simply by taking the average value of <math>y_{1}(i)-y_{0}(i)</math> across the sample. However, we can not observe both <math>y_{1}(i)</math> and <math>y_{0}(i)</math> for each individual since an individual cannot be both treated and not treated. For example, in the drug example, we can only observe  <math>y_{1}(i)</math> for individuals who have received the drug and <math>y_{0}(i)</math> for those who did not receive it. This is the main problem faced by scientists in the evaluation of treatment effects and has triggered a large body of estimation techniques.
 
If we could observe, for each individual, <math>y_{1}(i)</math> and <math>y_{0}(i)</math> among a large representative sample of the population, we could estimate the ATE simply by taking the average value of <math>y_{1}(i)-y_{0}(i)</math> across the sample. However, we can not observe both <math>y_{1}(i)</math> and <math>y_{0}(i)</math> for each individual since an individual cannot be both treated and not treated. For example, in the drug example, we can only observe  <math>y_{1}(i)</math> for individuals who have received the drug and <math>y_{0}(i)</math> for those who did not receive it. This is the main problem faced by scientists in the evaluation of treatment effects and has triggered a large body of estimation techniques.
   −
如果我们能观察到一个大型代表性样本中每个个体的<math> y _ {1}(i) </math> 和 <math> y _ {0}(i) </math> ,我们可以简单地通过取样本中 <math> y _ {1}(i)-y _ {0}(i) </math> 的平均值来估计平均处理效应。然而,我们不能同时观察每个个体的<math> y _ {1}(i)、y _ {0}(i) </math>,因为每个个体不能同时被处理和不被处理。例如,在药物例子中,我们只能观察到个体接受过药物治疗的<math> y _ {1}(i) </math> 和个体未接受药物的 <math> y _ {0}(i) </math> 。这是研究者们在评估治疗效果时面临的主要问题,并因此引发了大量的与估计方法相关的研究。
+
如果我们能观察到一个大型代表性样本中每个个体的<math> y _ {1}(i) </math> 和 <math> y _ {0}(i) </math> ,我们可以简单地通过取样本中 <math> y _ {1}(i)-y _ {0}(i) </math> 的平均值来估计平均处理效应。然而,我们不能同时观察每个个体的<math> y _ {1}(i)、y _ {0}(i) </math>,因为每个个体不能同时被处理和不被处理。例如,在药物例子中,我们只能观察到个体接受过药物治疗的<math> y _ {1}(i) </math> 和个体未接受药物的 <math> y _ {0}(i) </math> 。这是研究者们在评估治疗效果时面临的主要问题,并因此引发了大量与估计方法相关的研究。
    
== 估计 Estimation ==
 
== 估计 Estimation ==
252

个编辑