I'm trying to learn about Wald test.

I know, that its test statistics is

$$ t = \frac{\beta_i}{se\left( \beta_i \right)} $$

But, how is standard error $se$ computed in GLM? I've found only the case with linear model mentioned here.

I've also found some info on wiki, but its for the maximum likelihood estimator, so I'm not sure, what is different for the single coefficient.

And finally, I'm also interested in some estimation of the standard error, something like this eq.

$$ se = \frac{1}{\sqrt{I_n\left( \theta_{mle} \right)}}, $$

where $\theta_{mle}$ is the maximum likelihood estimator and $I_n$ is the Fisher information. This formula is also taken from the wiki-link.

I'd be glad to read a thorough explanation - I'm a complete beginner in statistics.


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