Theory and Methods of Statistics

3

Infinite Sequences of Random Variables and Their Convergence Properties

Abstract

In a problem of statistical inference if we use a statistic T_n based on a random sample $\left(X_1,\dots ,X_n\right)$, then it is important to know how T_n behaves as the sample size $n\to \infty$. Various modes of convergence of T_n and tools for proving such convergences are developed in this chapter.

Keywords

Modes of Convergence; Weak and Strong Laws of Large Numbers; Probability Inequalities.

3.1 Introduction

Let T be a statistic based on the data consisting of rv’s X₁, …, X_n. Most statistical ...