Estimation of a two‐component mixture model with applications to multiple testing

We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the other unknown distribution nonparametrically, given i.i.d. data from the mixture model. We use ideas from shape restricted function estimation and develop “tuning parameter free” estimators that are easily implementable and have good finite sample performance. We establish the consistency of our procedures. Distribution-free finite sample lower confidence bounds are developed for the mixing proportion. The identifiability of the model, and the estimation of the density of the unknown mixing distribution are also addressed. We discuss the connection with the problem of multiple testing and compare our procedure with some of the existing methods in that area through simulation studies. We also analyse two data sets, one arising from an application in astronomy and the other from a microarray experiment.

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