Abstract: We apply the modified likelihood ratio test to two binomial mixture models arising in genetic linkage analysis. The limiting distribution of the test statistic for both models is shown to be a mixture of chi-squared distributions. A consideration of random family sizes for both models gives similar results. We also explore the power properties under local alternatives. Simulation studies show that the modified likelihood ratio test is more powerful than other methods under a variety of model specifications.
Key words and phrases: Genetic linkage analysis, hypothesis testing, local asymptotic power, mixture models, modified likelihood, random family sizes, recombinant.