A random walk through Canadian contributions on empirical processes and their applications in probability and statistics

In this article, we present a review of important results and statistical applications obtained or generalized by Canadian pioneers and their collaborators, for empirical processes of independent and identically distributed observations, pseudo-observations, and time series. In particular, we consider weak convergence and strong approximations results, as well as tests for model adequacy such as tests of independence, tests of goodness-of-fit, tests of change point, and tests of serial dependence for time series. We also consider applications of empirical processes of interacting particle systems for the approximation of measure-valued processes.