16.1 Delta Method

• approximate the mean and variance of a function of random variables using a first-order Taylor approximation
• A semi-parametric method
• Alternative approaches:

  • Analytically derive a probability function for the margin

  • Simulation/Bootstrapping

• Resources:

  • Advanced: modmarg

  • Intermediate: UCLA stat

  • Simple: Another one

Let $G(\beta)$ be a function of the parameters $\beta$, then

$$var(G(\beta)) \approx \nabla G(\beta) cov (\beta) \nabla G(\beta)'$$

where

• $\nabla G(\beta)$ = the gradient of the partial derivatives of $G(\beta)$ (also known as the Jacobian)