Unlock: Delta Method

Asymptotic distribution of a smooth function of an estimator. If sqrt(n)(T_n - mu) converges to N(0, sigma^2), then sqrt(n)(g(T_n) - g(mu)) converges to N(0, [g'(mu)]^2 sigma^2). The multivariate version uses the Jacobian; the second-order version handles vanishing derivatives. The page derives the result, works three canonical examples (variance of a log proportion, variance of a ratio of means, asymptotic variance of the sample correlation), and ties the construction to variance-stabilizing transformations.