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

摘要

Simos Meintanis presents an interesting and useful survey of testing procedures based on the Empirical Characteristic Function (ECF). The ECF was originally introduced for parameter estimation of a stable law, i.e. in the situation where a description in terms of characteristic functions is much simpler than that in terms of distribution functions. It turned out, however, that there was a wide range of statistical problems where the ECF approach was a competitive alternative for other methods. Hypothesis testing, in particular, goodness-of-fit testing and testing in the two-sample problem, is among these problems, and the survey under discussion gives a lot of helpful information.In this discussion I review some results of two problems concerning statistical testing based on the ECF. The first problem is testing independence, where the ECF turns out to be a very powerful tool, and where a number of remarkable results have been obtained during the last decade. The second problem concerns goodness-of-fit testing based on the ECF and is connected with the fact that the data are always given in the discretized form and this often must be taken into account.