Pairwise rank based likelihood for estimating the relationship between two homogeneous populations and their mixture proportion
نویسنده
چکیده
We consider the problem of inferring the relationship between two homogeneous populations, and the prevalence of each population. Sample data from the two distributions as well as from a third population consisting of a mixture of the two will be used. Under the transformation model assumption on the two distribution functions, we develop a pairwise rank based likelihood. Simultaneous inference on the mixture proportion and the transformation parameter defining the relationship between the two populations is based on this likelihood. Under some regularity conditions, it is shown that the maximum pairwise rank likelihood estimator is consistent and has an asymptotic normal distribution. Simulation results indicate that the performance of this statistic is satisfactory. The methodology is demonstrated on a data set in prostate cancer.
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