I'm reading the book: All of statistics, by Wasserman, and I think the author wasn't very clear in the definition of the Wald's test on page 153:
10.3 Definition. The Wald Test
Consider testing
$H_0:\theta = \theta_0\ \text{versus}\ H_1 : \theta = \theta_ 0$
Assume that $\hat{\theta}\ \text{is asymptotically Normal:}$
$\frac{\hat\theta-\theta_0}{\hat {se}}\xrightarrow{(d)} \mathcal N(0,1)$
The size $\alpha$ Wald test is: reject $H_0$ when $|W|>z_{\alpha/2}$ where
$W=\frac{\hat{\theta}-\theta_0}{\hat{se}}$
The author shouldn't have write:
10.3 Definition. The Wald Test
Consider testing
$H_0:\theta = \theta_0\ \text{versus}\ H_1 : \theta = \theta_ 0$
If $H_0$ is true, assume that $\hat{\theta}\ \text{is asymptotically Normal:}$
$\frac{\hat\theta-\theta_0}{\hat {se}}\xrightarrow{(d)} \mathcal N(0,1)$
The size $\alpha$ Wald test is: reject $H_0$ when $|W|>z_{\alpha/2}$ where
$W=\frac{\hat{\theta}-\theta_0}{\hat{se}}$
I'm a little confused