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Related Models

  • Debasis Kundu
  • Swagata Nandi
Chapter
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Abstract

The sinusoidal frequency model is a well-known model in different fields of science and technology and as has been observed in previous chapters, it is a very useful model for explaining nearly periodical data. There are several other models which are practically the multiple sinusoidal model, but also exploit some extra features in the data. In most of such cases, the parameters satisfy some additional conditions other than the assumptions required for the sinusoidal model. For example, if the frequencies appear at \(\lambda , 2\lambda , \ldots , p\lambda \) in a multiple sinusoidal model, then the model that exploits this extra information is the fundamental frequency model. The advantage of using this information in the model itself is that it reduces the total number of parameters to \(2p+1\) from \(3p\) and a single non-linear parameter instead of \(p\), in case of multiple sinusoidal model. Similarly, if the gap between two consecutive frequencies is approximately same, then the suitable model is the generalized fundamental frequency model. We call these models as “related models” of the sinusoidal frequency model.

Keywords

Fundamental Frequency Asymptotic Variance Strong Consistency Frequency Model Sinusoidal Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Debasis Kundu
    • 1
  • Swagata Nandi
    • 2
  1. 1.Department of Mathematics and StatisticsIndian Institute of TechnologyKanpurIndia
  2. 2.Theoretical Statistics and Mathematics UnitIndian Statistical InstituteNew DelhiIndia

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