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Inferential Statisticshard
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Suppose an estimator θ^n\hat{\theta}_nθ^n​ for a parameter θ\thetaθ is based on nnn samples and satisfies n(θ^n−θ)→dN(0,V(θ))\sqrt{n}(\hat{\theta}_n - \theta) \xrightarrow{d} N(0, V(\theta))n​(θ^n​−θ)d​N(0,V(θ)). If we are interested in the asymptotic distribution of the transformation g(θ)=θkg(\theta) = \theta^kg(θ)=θk for θ>0\theta > 0θ>0, what does the Delta Method specify as the asymptotic variance of n(g(θ^n)−g(θ))\sqrt{n}(g(\hat{\theta}_n) - g(\theta))n​(g(θ^n​)−g(θ))?