Multivariate Wald statistic

For a regular $p$-parameter model, the Wald statistic for a candidate $\theta$ isUnder the true parameter it converges in distribution to ${\chi }_p^2$.

For a full-row-rank $k\times p$ matrix $R$ and the null hypothesis $R\theta =r$, putUnder the null, asymptotic normality and Slutsky theorem give $W_{n,R}\stackrel{d}{\to }{\chi }_k^2$.