An analysis of tests against nonparametric alternatives in exponential mixture models
Wilfried Seidel, Hana Ševčíková · 2003
To test for homogeneity or for the number of components in a mixture model, LR tests against a nonparametric alternative hypothesis are developed. Their performance depends on the strategies for likelihood maximization. A fast and statistically powerful combination of methods under the null and under the alternative hypothesis is proposed, it includes elimination of spurious components. A sequence of tests is applied for assessing the number of components and its performance is analyzed in a number of simulation studies in exponential mixture models. Although critical values have to be bootstrapped, the probability of overestimating is still bounded by the nominal level of the individual tests. Taking into account the number of components that can be reliably detected on basis of a certain sample size, the proposed procedure yields the minimum number of components that is needed for an adequate representation of the sample.