The pre-classical asymptotic theory of statistics discussed such facts as the weak law of large numbers, which states that as our amount of data grows (assuming independence between data points) our sample mean converges to the true mean. The big question that remained at the forefront of everyone’s minds was “but how quickly does the convergence happen?” since we will never truly have infinite data. This led to a significant interest in proving central limit theorems, which deal with exactly this topic. It is this asymptotic theory that rescues probability and statistics from merely being a tool for games of chance to being the central tool for how scientists analyze the world around us.
This playlist by Ben Lambert discusses the asymptotic theory of estimators and only requires an understanding of calculus, plus knowledge of what a random variable and an expected value is. Enjoy!