36-760 Central Limit Theorems

6 units, Carnegie Mellon University

Central limit theorems form the backbone of statistical inference. Classical central limit theorems prove convergence in distribution of scaled averages of independent random variables to a normal random variable. More generally, convergence to any distribution can be considered a limit theorem. In the first part of the course, we will discuss central limit theorems for a variety of functions of independent and dependent random variables. We will also consider asymptotic expansions such as Edgeworth expansions briefly. One of the main intuitions for the central limit theorem is that any statistic function of n variables that is not strongly influenced by any one of the variables should approach a limit asymptotically. We will see how this intuition plays out in several examples. There is no single book we follow for this. The course material is taken from several works of Bentkus, Gotze, Friedrich, Paulauskas, and Rackauskas.

Prerequisites: none listed

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