Asymptotics

The Delta Method

Deriving the delta method from a Taylor expansion and simulating its use for variance stabilizing transformations of Poisson and exponential data and for standard errors in polynomial regression.

Convergence In Probability

Working through the definition of convergence in probability from Casella and Berger, using Chebyshev's inequality to show the weak law of large numbers for the sample mean and variance, and simulating normal samples to watch both estimates converge.