Estimating the Statistical Power of the Benjamini Hochberg Procedure
In this work we investigate the properties of the statistical power of the Benjamini Hochberg procedure. That procedure provides a widely used method for controlling the False Discovery Rate in a multiple comparison setup. We show that in many cases the statistical power of the p values adjusted by the Benjamini Hochberg procedure could be approximated by a normal distribution with both its mean and standard deviation having an exponential fit and convergence when the number of tests increase. As a result one could estimate the probability that the power belongs in a predetermined interval in a very computationally efficient way using only simulations for several values of the number of tests parameter. The fit for the mean also supports the conjecture that the power of the test decreases to the limit power, which is known to exist, when increasing the number of tests. The latter is a very favourable observation from practical perspective and we try to offer partially rigorous explanation why the monotonicity is present.
HPC