Let's say we know this:
[tex]
\sqrt{n}\left(\widehat{\theta} - \theta\right) \sim \mathcal{N}\left(0, \frac{1}{F(\theta)}\right)
[/tex]
How do we get from this information to this expression of confidence interval for [itex]\theta[/itex]?
[tex]
\left( \widehat{\theta} \pm u_{1-\frac{\alpha}{2}}\frac{1}{\sqrt{nF\left(\widehat{\theta}\right)}}\right )
[/tex]
Where [itex]u_{1-\frac{\alpha}{2}}[/itex] is appropriate quantil of standard normal distribution.
Thank you.
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