Mean-square risk of the FDR procedure under weak dependence

In many application areas, the problem of processing large amounts of data arises. In this case, before processing, the data array is often subjected to some transformation leading to a “sparse” or “economical” representation in which the absolute value of most elements of the array is equal to zero (or sufficiently small). In addition, as a result of interference when receiving and transmitting data, they become corrupted with noise and it is desirable to remove this noise during further processing. The resulting task is mathematically equivalent to some multiple hypothesis testing problems. Previously, to solve this problem under conditions of normality, independence, and sparsity of data, a procedure based on the method of controlling the average proportion of erroneously rejected hypotheses was proposed (False Discovery Rate, FDR). In this paper, the authors study the asymptotics of the mean-square risk of this procedure in the case of a weak dependence in the data.