Modes of Convergence

Abstract

In this chapter we discuss different types of convergence in probability and statistics. Types of convergence have already been introduced. They are convergence in probability and convergence in distribution. In addition, we introduce other types of convergence, such as almost sure convergence and L ^p convergence. We discuss properties of different types of convergence, the connections between them, and how to establish these properties. The discussion will mainly focus on the case of univariate random variables. However, most of the results presented here can be easily extended to the multivariate situation.