Hypothesis testing under mixture models: Application to genetic linkage analysis

In this paper we propose a new class of statistics to test a simple hypothe sis against a family of alternatives characterized by a mixture model. Unli ke the likelihood ratio statistic, whose large sample distribution is still unknown in this situation, these new statistics have a simple asymptotic d istribution to which to refer under the null hypothesis. Simulation results suggest that it has adequate power in detecting the alternatives. Its appl ication to genetic linkage analysis in the presence of the genetic heteroge neity that motivated this work is emphasized.