Background: False discovery rate (FDR) methods play an important role in analyzing highdimensional data. There are two types of FDR, tail area-based FDR and local FDR, as well as numerous statistical algorithms for estimating or controlling FDR. These differ in terms of underlying test statistics and procedures employed for statistical learning. Results: A unifying algorithm for simultaneous estimation of both local FDR and tail area-based FDR is presented that can be applied to a diverse range of test statistics, including p-values, correlations, z- and t-scores. This approach is semipararametric and is based on a modified Grenander density estimator. For test statistics other than p-values it allows for empirical null modeling, so that dependencies among tests can be taken into account. The inference of the underlying model employs truncated maximum-likelihood estimation, with the cut-off point chosen according to the false non-discovery rate. Conclusion: The proposed procedure gene...