Table of Contents
1. Univariate Delta Method
For a sequence of random variables \(X_n\) satisfying the convergence in distribution: \[ \sqrt{n}(X_n - \theta) \stackrel{D}{\rightarrow} \mathcal{N}(0, \sigma^2), \]
Then \[ \sqrt{n}(g(X_n) - g(\theta) )\stackrel{D}{\rightarrow} \mathcal{N}(0, \sigma^2\cdot (g'(\theta))^2) \] for any function \(g\) if \(g'(\theta)\) exists and non-zero.