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

Abstract

AbstractIn 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.