Nonparametric inference and confidence intervals

Now that we have a basis in probability theory, we proceed to statistical inference. One of the most widely used concepts in statistical inference is the plug-in principle. In fact, you have probably employed it countless times but didn’t even realize it! In what follows, we will formally define the plug-in principle and the important concept of confidence intervals for our first foray into inference.

Specifically, we will learn about how to perform statistical inference when we do not have a generative model in mind. Because there is no generative model, there are no parameters, and, as such, this class of inference problems are referred to as nonparametric. As you may have guessed, we will employ the plug-in principle to use the empirical distribution as an approximation for the unknown true generative distribution.