A conservative estimator for the proportion of false nulls based on Dvoretzky, Kiefer and Wolfowitz inequality

We propose a simple estimator for the weight in a two-component mixture model between a known and an unknown density. We make no parametric assumptions about the unknown component and estimate the weight conservatively, i.e., the estimate is smaller than the true value with high probability. A brief simulation is used to compare the proposal with already available conservative approaches.