There is a potential issue on chapter 21, in the following paragraph
Here, they plot the difference between the true causal effect (red outline) and the estimated causal effect,
$\tau - \hat{\tau}$, using an S-learner. The estimated causal effect is heavily downward biased ( $\tau - \hat{\tau} \gt 0$ most of the time). In other words, the true causal effect is frequently bigger than the estimated one.
Improvement:
Here, they plot the difference between the estimated causal effect and the true causal effect (red outline),
$\hat{\tau} - \tau$, using an S-learner. The estimated causal effect is heavily biased ( $\hat{\tau} - \tau \gt 0$ most of the time).
Explanation:
The paper mentions the plot shows simulated distribution for estimator $\hat{\theta{0}} - \theta{0}$ (centered at true value $\theta_{0}$) and the simulated distribution is shifted right compared to a normal approximation derived under the assumption of no bias.
Guessing the causal effect found was negative so regularization biasing the treatment effect to 0 means a positive difference when subtracting the true value from the ml estimated one. This makes this part of the text confusing in this passage since it mentions a downward bias but shows a positive difference in the plot.
I'm not quite sure the best way to re-word this or if this interpretation is correct. If not, let me know and I'm sure this will be a good learning experience.
matheusfacure
commented
1 year ago
There is a potential issue on chapter 21, in the following paragraph
Here, they plot the difference between the true causal effect (red outline) and the estimated causal effect, $\tau - \hat{\tau}$, using an S-learner. The estimated causal effect is heavily downward biased ( $\tau - \hat{\tau} \gt 0$ most of the time). In other words, the true causal effect is frequently bigger than the estimated one.
Improvement:
Here, they plot the difference between the estimated causal effect and the true causal effect (red outline), $\hat{\tau} - \tau$, using an S-learner. The estimated causal effect is heavily biased ( $\hat{\tau} - \tau \gt 0$ most of the time).
Explanation:
The paper mentions the plot shows simulated distribution for estimator $\hat{\theta{0}} - \theta{0}$ (centered at true value $\theta_{0}$) and the simulated distribution is shifted right compared to a normal approximation derived under the assumption of no bias. Guessing the causal effect found was negative so regularization biasing the treatment effect to 0 means a positive difference when subtracting the true value from the ml estimated one. This makes this part of the text confusing in this passage since it mentions a downward bias but shows a positive difference in the plot. I'm not quite sure the best way to re-word this or if this interpretation is correct. If not, let me know and I'm sure this will be a good learning experience.