Consider Pearson’s correlation coefficient, \(r\), calculated from two variables \(X\) and \(Y\) with population correlation \(\rho\). If one calculates \(r\) from a simple random sample of \(N\) observations, then its sampling variance will be approximately
The delta method is surely one of the most useful techniques in classical statistical theory. It’s perhaps a bit odd to put it this way, but I would say that the delta method is something like the precursor to the bootstrap, in terms of its utility and broad range of applications—both are “first-line” tools for solving statistical problems.
I just covered instrumental variables in my course on causal inference, and so I have two-stage least squares (2SLS) estimation on the brain. In this post I’ll share something I realized in the course of prepping for class: that standard errors from 2SLS estimation are equivalent to delta method standard errors based on the Wald IV estimator.