Nonparametric testing of distributions—the Epps–Singleton two-sample test using the empirical characteristic function
Sebastian J. Goerg
Max Planck Institute for Research on Collective Goods
Kurt-Schumacher-Straße 10
53113 Bonn, Germany
goerg@coll.mpg.de
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Johannes Kaiser
Deutsche Bundesbank
Wilhelm-Epstein-Straße 14
60431
Frankfurt, Germany
johannes.kaiser@bundesbank.de
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Abstract. In statistics, two-sample tests are used to determine whether two samples
have been drawn from the same population. An example of such a test is the
widely used Kolmogorov–Smirnov two-sample test. There are other distributionfree
tests that might be applied in similar occasions. In this article, we describe a
two-sample omnibus test introduced by Epps and Singleton, which usually has a
greater power than the Kolmogorov–Smirnov test although it is distribution free.
The superiority of the Epps–Singleton characteristic function test is illustrated in
two examples. We compare the two tests and supplement this contribution with
a Stata implementation of the omnibus test.
View all articles by these authors:
Sebastian J. Goerg, Johannes Kaiser
View all articles with these keywords:
escftest, nonparametric tests, Kolomogorov–Smirnov, Epps–Singleton, two-sample case
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