Testing Against Nonparametric Alternatives in Mixture Models
Wilfried Seidel, Hana Ševčíková, Krunoslav Sever · Journal of Computational and Graphical Statistics · 2007
Likelihood ratio tests in parametric mixture models suffer from several sources of instability, therefore tests against a nonparametric alternative are proposed. Their performance depends on the strategies for likelihood maximization. This article develops a fast and statistically powerful combination of methods under the null hypothesis and under the alternative hypothesis; the method also includes elimination of spurious components.Modifying a strategy proposed by McLachlan, a sequence of such 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 the basis of a certain sample size, the proposed procedure yields the minimum number of components that is required for an adequate representation of the sample. It is compared to methods based on the Bayesian and the Akaike information criterion, and a recommendation is given to identify a range of meaningful model orders compatible with a given sample.