Wald statistic = z-value? I'm doing an assignment in R for my inference theory class and i'm a bit stuck here.
I have been given a summary of some model and im being asked to confirm that the z-value is equal to the wald statistic.
The wald statistic is according to our book:
$\sqrt{I(\theta_{NR)}} \cdot (\theta_{NR}-\theta_0)$
where  $\theta_{NR}$ is a theta value of the regression variables which was retrieved from a Newton-Raphson function and $\theta_0$ is a vector of equal length of $\theta_{NR}$ which only contains zeros and $I()$ is the function for the fisher's information matrix.
Well i thought that i could write a function that calculates the fishers matrix and then simply use it in the formula for the wald statistic but it wont produce the right results. Maybe i have interpreted the formula wrong?
any ideas anyone?
the code for the fishers matrix is confirmed to be working btw! :)
 A: Maybe you have got it already. Otherwise, check page 99 in the book (i guess we are in the same class haha), where you may find that $se(\theta_{NR})=\frac{1}{\sqrt{I(\theta_{NR})}}$. We have already calculated the standard deviation $se(\theta_{NR})$ in laboration part I. So you may just take $\frac{1}{se(\theta_{NR})}$ and multiply it by $\theta_{NR}$ to get the z-values :)
A: A Wald statistic is not endemic to Newton Raphson estimation. It is a particular statistic formed with a parameter estimate and its standard error.
A Z-statitic is something that takes a standard normal distribution.
Wald statistics rarely take standard normal distributions, except in the case of a one sample z-test (variance known) for normally distributed data when the null hypothesis $\mu=0$ is true. The Wald stat, however, has important limit theorems that might relate the two values.
When we do inference, we compare a Wald stat with a distribution it might be expected to take. For most estimates, $W = \hat{\theta}/se(\hat{\theta})$ has an asymptotically normal 0, 1 distribution under the null hypothesis.
As stated your problem, results, and approach do not line up.
