An Introduction to Copulas: a Complement

TL;DR

This paper provides a concise, complementary introduction to copula theory aimed at advanced statistics students, aligning with Casella and Berger's style to fill a notable gap in their textbook.

Contribution

It adds two sections on copulas to an existing statistical inference course, maintaining consistency with the original text's style and structure.

Findings

Introduces copula concepts in a style consistent with Casella and Berger (2002).

Provides a stand-alone, brief introduction to copula theory.

Complements existing statistical inference education with new copula material.

Abstract

For many years I have taught an advanced statistical inference course for master's students using the text of Casella and Berger (2002). The book gives a comprehensive treatment of the core topics at a level that avoids measure theory while remaining mathematically precise, but it does not cover the increasingly important concept of copulas. The present notes are intended to complement the book by adding two sections on copulas in a style that is as close as possible to that of the original text. Numbering of definitions, theorems, examples, and exercises is consistent with Casella and Berger (2002), but the material may also be read as a brief, stand-alone introduction to copula theory.