Direct deconvolution density estimation of a mixture distribution motivated by mutation effects distribution

The mutation effect distribution is essential for understanding evolutionary dynamics. However, the existing studies on this problem have had limited resolution. So far, the most widely used method is to fit some parametric distribution, such as an exponential distribution whose validity has not been checked. In this paper, we propose a nonparametric density estimator for the mutation effect distribution, based on a deconvolution approach. Consistency of the estimator is also established. Unlike the existing deconvolution estimators, we cover the case that the target variable has a mixture structure with a pointmass and a continuous component. To study the property of the proposed estimator, several simulation studies are performed. In addition, an application for modelling virus mutation effects is provided.