Limit theorems for dissociated random variables

Abstract

Families of exchangeably dissociated random variables are defined and discussed. These include families of the form g(Yi, Yj, …, Yz) for some function g of m arguments and some sequence Yn of i.i.d. random variables on any suitable space. A central limit theorem for exchangeably dissociated random variables is proved and some remarks on the closeness of the normal approximation are made. The weak convergence of the empirical distribution process to a Gaussian process is proved. Some applications to data analysis are discussed.