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Inferential Statisticshard
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Consider a sequence of estimators θ^n\hat{\theta}_nθ^n​ such that 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)). According to the Delta Method, if we apply a transformation g(θ)=ln⁡(θ)g(\theta) = \ln(\theta)g(θ)=ln(θ) (for θ>0\theta > 0θ>0), what is the asymptotic distribution of n(ln⁡(θ^n)−ln⁡(θ))\sqrt{n}(\ln(\hat{\theta}_n) - \ln(\theta))n​(ln(θ^n​)−ln(θ))?