Central Limit Theorem: Multivariate Delta Method

This lecture covers the Central Limit Theorem, Slutsky's Theorem, and the Multivariate Delta Method, explaining how different types of convergence in probability and distribution work. The instructor discusses the continuous mapping theorem, joint convergence, and the Cramér-Wold device, providing insights into the convergence of random variables and vectors. The lecture also delves into the multivariate Law of Large Numbers and the approximation of distributions using Gaussian distributions. Additionally, the Delta Method in the multivariate case is explored, highlighting the importance of the Jacobian matrix in determining the limiting distribution of multivariate functions of random variables.