Wald Test

• Wald Test Wikipedia_on_multiple_parameters)

$$\hat{\beta} - \beta \sim \mathcal{N}(0, \Sigma)$$

and the hypothesis test is,

$$H_0: f(\beta) = 0$$

The covariance matrix of $f(\beta)$ can be constructed using Delta method and

$$f(\beta)^{\prime}[\operatorname{var}(f(\beta))]^{-1} f(\beta) \sim^{a} \chi^{2}(q)$$