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Inferential Statisticshard
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Consider a sequence of estimators θ^n\hat{\theta}_nθ^n​. If n(θ^n−θ)→dN(0,V)\sqrt{n}(\hat{\theta}_n - \theta) \xrightarrow{d} N(0, V)n​(θ^n​−θ)d​N(0,V), what is the asymptotic distribution of n(θ^n2−θ2)\sqrt{n}(\hat{\theta}_n^2 - \theta^2)n​(θ^n2​−θ2) assuming θ>0\theta > 0θ>0?