What Intraclass Covariance Structures Can Symmetric Bernoulli Random Variables Have?

TL;DR

This paper characterizes the possible intraclass covariance matrices for symmetric Bernoulli variables, revealing the structure and constraints of such covariances in this specific binary setting.

Contribution

It provides a novel characterization of intraclass covariance matrices specifically for symmetric Bernoulli variables, a case not thoroughly understood before.

Findings

Characterization of feasible covariance matrices for symmetric Bernoulli variables

Identification of constraints on covariances in the symmetric Bernoulli case

Potential implications for modeling binary data with intraclass structures

Abstract

The covariance matrix of random variables $X_1,\dots,X_n$ is said to have an intraclass covariance structure if the variances of all the $X_i$'s are the same and all the pairwise covariances of the $X_i$'s are the same. We provide a possibly surprising characterization of such covariance matrices in the case when the $X_i$'s are symmetric Bernoulli random variables.