# delta method

## Sampling variance of Pearson r in a two-level design

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 multivariate delta method

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.

## 2SLS standard errors and the delta-method

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.