Let's say we know this:(adsbygoogle = window.adsbygoogle || []).push({});

[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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# Confidence interval

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