15.1 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)