The Simultaneous Estimation of the Number of Signals and Frequencies of Multiple Sinusoids When Some Observations Are Missing: I. Asymptotics

The problem of simultaneous estimation of the number of signals and frequencies of multiple sinusoids is considered in the case when some observations are missing. The number of signals is estimated with an information theoretic criterion, and the frequencies are estimated with eigen-variation linear prediction. The strong consistency of the estimates of the number of signals and the frequencies is established and the rate of convergence of these estimates is provided. Besides, the limiting distributions of various estimates are given.