An inverse Laplace transform oracle estimator for the normal means problem.

In an effort to estimate the number of true nulls in large scale multiplicity problems (the normal means problem), we generalize the current Fourier transform based oracle estimator with a Laplace transform based estimator. Our interest in this problem stems from the application of r-power which requires knowledge of the number of nulls (Dasgupta et al. in Sankhya B 78(1):96–118, 2016). We analytically show that our method is consistent and theoretically has lower mean squared error than the existing competitor (Jin in J R Stat Soc Ser B (Stat Methodol) 70(3):461–493, 2008). We follow up by a numerical example and a simulation study that ratifies our theoretical results. [ABSTRACT FROM AUTHOR]