On the sparsity of signals in a random sample

This article proposes a method of moments technique for estimating the sparsity of signals in a random sample. This involves estimating the largest eigenvalue of a large Hermitian trigonometric matrix under mild conditions. As illustration, the method is applied to two well-known problems. The first focuses on the sparsity of a large covariance matrix and the second investigates the sparsity of a sequence of signals observed with stationary, weakly dependent noise. Simulation shows that the proposed estimators can have significantly smaller mean absolute errors than their main competitors.