Comments: A review of testing procedures based on the empirical characteristic function

摘要

It is a nicely and clearly written paper on statistical procedures based on the empirical characteristic function (ECF). The paper provides an overview of recently developed goodness-of-fit tests based on functionals of the ECF for both simple setups as well as rather advanced situations (with nuisance parameters). The author also touches on procedures based on the ECF for the k-sample problem. In this discussion I would like to bring attention to another class of procedures based on the ECFs used in change point analysis, that is, a class of statistical procedures for the detection of instabilities in various statistical models based on functionals of the ECFs.