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We consider a two-component mixture model with one known component. Wedevelop methods for estimating the mixing proportion and the unknowndistribution nonparametrically, given i.i.d.~data from the mixture model, usingideas from shape restricted function estimation. We establish the consistencyof our estimators. We find the rate of convergence and asymptotic limit of theestimator for the mixing proportion. Completely automated distribution-freehonest finite sample lower confidence bounds are developed for the mixingproportion. Connection to the problem of multiple testing is discussed. Theidentifiability of the model, and the estimation of the density of the unknowndistribution are also addressed. We compare the proposed estimators, which areeasily implementable, with some of the existing procedures through simulationstudies and analyse two data sets, one arising from an application in astronomyand the other from a microarray experiment.

Estimation of a Two-component Mixture Model with Applications to Multiple Testing