Thread: Confidence interval View Single Post
 P: 368 Let's say we know this: $$\sqrt{n}\left(\widehat{\theta} - \theta\right) \sim \mathcal{N}\left(0, \frac{1}{F(\theta)}\right)$$ How do we get from this information to this expression of confidence interval for $\theta$? $$\left( \widehat{\theta} \pm u_{1-\frac{\alpha}{2}}\frac{1}{\sqrt{nF\left(\widehat{\theta}\right)}}\right )$$ Where $u_{1-\frac{\alpha}{2}}$ is appropriate quantil of standard normal distribution. Thank you.