Summary: Interval mapping of quantitative trait loci from breeding experiments plays an important role in understanding the mechanisms of disease, both in humans and other organisms. Standard approaches to estimation involve parametric assumptions for the component distributions and may be sensitive to model misspecification. Some nonparametric tests have been studied. However, nonparametric estimation of the phenotypic distributions has not been considered in the genetics literature, even though such methods might provide essential nonparametric summaries for comparing different loci.
We develop a sufficient condition for identifiability of the phenotypic distributions. Simple nonparametric estimators for the distributions are proposed for uncensored and right censored data. They have a closed form and their small and large sample properties are readily established. Their practical utility as numerical summaries which complement nonparametric tests is demonstrated on two recent genetics examples.