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Abstract: A procedure to estimate a two-component mixture model where one component is known is proposed. The unknown part is estimated with a weighted kernel function. The weights are defined in an adaptive way. The convergence to a unique solution of our estimation procedure is proven. The procedure is compared with two classical approaches using simulation. In addition, the results obtained are applied to multiple testing procedure in order to estimate the posterior population probabilities and the local false discovery rate. [Copyright &y& Elsevier]