Inferential Statisticshard
0:00.0

Suppose an estimator θ^n\hat{\theta}_n for a parameter θ\theta is based on nn samples and satisfies n(θ^nθ)dN(0,V(θ))\sqrt{n}(\hat{\theta}_n - \theta) \xrightarrow{d} N(0, V(\theta)). If we are interested in the asymptotic distribution of the transformation g(θ)=θkg(\theta) = \theta^k for θ>0\theta > 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))?