Asymptotic normality and strong consistency of risk estimate when using the FDR threshold under weak dependence condition

An approach to solving the problem of noise removal in a large array of sparse data is considered based on the method of controlling the average proportion of false hypothesis rejections (False Discovery Rate, FDR). This approach is equivalent to threshold processing procedures that remove array components whose values do not exceed some specified threshold. The observations in the model are considered weakly dependent. To control the degree of dependence, restrictions on the strong mixing coefficient and the maximum correlation coefficient are used. The mean-square risk is used as a measure of the effectiveness of the considered approach. It is possible to calculate the risk value only on the test data; therefore, its statistical estimate is considered in the work and its properties are investigated. The asymptotic normality and strong consistency of the risk estimate are proved when using the FDR threshold under conditions of weak dependence in the data.