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wald test and score test, normal or chi square?

I learnt from section 10.3 of statistical inference that both Wald test statistic $\frac{W_n-\theta_0}{S_n}\approx\frac{W_n-\theta_0}{\sqrt{\hat I_n(W_n)}}$ and score test statistic $\frac{S(\theta_0)}...
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