\(\displaystyle I^{-\frac{1}{2}} U \approx N(0,1) \)

and

\(\displaystyle I^{\frac{1}{2}}(\widetilde{\theta}-\theta)\approx N(0,1) \)

I is fisher information, \(\displaystyle \widetilde{\theta} \) is mle

how to prove these two arguments

and

\(\displaystyle I^{\frac{1}{2}}(\widetilde{\theta}-\theta)\approx N(0,1) \)

I is fisher information, \(\displaystyle \widetilde{\theta} \) is mle

how to prove these two arguments

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