Inferential Statisticshard
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Consider a sequence of estimators (\hat{\theta}_n) for a parameter (\theta_0). Suppose (\sqrt{n}(\hat{\theta}_n - \theta_0) \xrightarrow{d} N(0, V)) and we define a transformation (g(\theta)) that is differentiable at (\theta_0) with (g'(\theta_0) = 0). Under these conditions, what is the asymptotic distribution of (n(g(\hat{\theta}_n) - g(\theta_0))) and what is the primary consequence for the standard Delta Method?
Consider a sequence of estimators (\hat{\theta}_n) for a parameter (\theta_0). Suppose (\sqrt{n}(\hat{\theta}_n - \theta_0) \xrightarrow{d} N(0, V)) and we define a transformation (g(\theta)) that is differentiable at (\theta_0) with (g'(\theta_0) = 0). Under these conditions, what is the asymptotic distribution of (n(g(\hat{\theta}_n) - g(\theta_0))) and what is the primary consequence for the standard Delta Method?