On Simultaneous Estimation of the Number of Signals and Frequencies of Multiple Sinusoids When Some Observations Are Missing |
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Authors: | C R Rao Y Wu |
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Institution: | 1. Department of Statistics , Pennsylvania State University , University Park , Pennsylvania , USA;2. Department of Mathematics and Statistics , York University , Toronto , Ontario , Canada |
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Abstract: | In an earlier article (Bai et al., 1999
Bai , Z. D. ,
Rao , C. R. ,
Wu , Y. H. ,
Zen , M. M. ,
Zhao , L. C. ( 1999 ). The simultaneous estimation of the number of signals and frequencies of multiple sinusods when some observations are missing: I. Asymptotics . Proc. Natl. Acad. Sci. 96 : 11,106 – 11,110 . CSA] Crossref], Web of Science ®] , Google Scholar]), the problem of simultaneous estimation of the number of signals and frequencies of multiple sinusoids is considered in the case that some observations are missing. The number of signals is estimated with an information theoretic criterion and the frequencies are estimated with eigenvariation linear prediction. Asymptotic properties of the procedure are investigated but the Monte Carlo simulation is not performed. In this article, a slightly different but scale invariant criterion for detection is proposed and the estimation of frequencies remains the same. Asymptotic properties of this new procedure are provided. Monte Carlo Simulation for both procedures is carried out. Furthermore, comparison on the real signals is also given. |
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Keywords: | Estimation Frequencies Limiting distribution Multiple sinusoids Number of signals Signal processing Strong consistency |
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