EM algorithm and its application to testing hypotheses

The conventional method for testing hypotheses is to find an exact or asymptotic distribution of a test statistic. But when the model is complex and the sample size is small, difficulty often arises. This paper aims to present a method for finding maximum probability with the help of EM algorithm. For any fixed sample size, this method can be used not only to obtain an accurate test but also to check the real level of a test which is build by large sample theory. Especially, while doing this, one needs neither the accurate nor asymptotic distribution of the test statistic. So the method is easily performed and is especially useful for small samples.