In Poisson and negative binomial regression, the response is assumed have Poisson and negative binomial distributions respectively. When we test the significance of the parameter $\beta$, which is estimated by maximum likelihood estimation, we have the Wald chi-squared statistic
$\left(\frac{\beta}{\text{standard error}(\beta)}\right)^2$.
The questions are:
- How to derive this Wald chi-squared statistic from the response distribution assumption?
- How to derive the standard error for this case?