Ononot — In the context of the Wald test for H0: \theta = \theta0, su

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Inferential Statisticshard

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In the context of the Wald test for $H_0: \theta = \theta_0$ , suppose the estimator $\hat{\theta}_n$ follows $\sqrt{n}(\hat{\theta}_n - \theta) \xrightarrow{d} N(0, V(\theta))$ . If the null hypothesis is true, what is the asymptotic behavior of the Wald statistic $W_n = n(\hat{\theta}_n - \theta_0)^T [V(\hat{\theta}_n)]^{-1}(\hat{\theta}_n - \theta_0)$ ?