Consistency of two detection techniques using single measurement of data

In this paper, we prove the (large sample) strong consistency of two methods for detection of frequencies using a single measurement. The two methods are the efficient detection criterion (EDC) by Zhao et al., and the alternating notch periodogram approach (ANPA) by Hwang-Chen. The strong consistency of the two methods using a single measurement was claimed but not proved by Hwang-Chen. Furthermore, this paper provides a class of sufficient conditions for strong consistency, which in part contradicts that claimed by Hwang-Chen.