How to use the functional empirical process for deriving asymptotic laws for functions of the sample

TL;DR

This paper explains how to use the functional empirical process to derive asymptotic laws for sample-based functions, providing a clear description, justification, and an illustrative example with bivariate data.

Contribution

It offers a comprehensive yet concise explanation of the functional empirical process method and demonstrates its application with a non-trivial bivariate data example.

Findings

The method effectively derives asymptotic laws for complex statistics.

The paper provides a justified framework for applying the functional empirical process.

An illustrative example with bivariate data showcases practical application.

Abstract

The functional empirical process is a very powerful tool for deriving asymptotic laws for almost any kind of statistics whenever we know how to express them into functions of the sample. Since this method seems to be applied more and more in the very recent future, this paper is intended to provide a complete but short description and justification of the method and to illustrate it with a non-trivial example using bivariate data. It may also serve for citation without repeating the arguments.