# Simulation for CI, Reflecting Quantiles

I was reading Hogg/Craig and my course notes and encountered a subsection on simulation to find out Confidence Intervals. The method expressed is to generate a random sample, calculate the MLE, repeat a billion times, find upper and lower $\alpha/2$ quantiles for the empirical distribution of the MLE. (Call them $l$ and $u$.)

Then, it said that a crude CI for the MLE would be $\hat{\theta}\pm z_{\alpha/2} SE(\hat{\theta})$. I understood everything till her. Now, they said, that a better estimate would be :

$$\hat{\theta} \in (2\hat{\theta}-u,2\hat{\theta}-l)$$ and added that this is called "reflecting quantiles". I don't appreciate

• Why this is a CI in the first place?
• How is this better?
• What is the rationale behind this?
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