Skip to main content

Estimating the Number of Components

  • Chapter
  • First Online:
Book cover Statistical Signal Processing

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST))

  • 2470 Accesses

Abstract

In the previous two chapters, we have discussed different estimation procedures of model (3.1) and properties of these estimators. In all these developments, it has been assumed that the number of components ā€˜pā€™ is known in advance. But in practice estimation of p is also a very important problem. Although, during the last 35 to 40 years extensive work has been done in estimating the frequencies of model (3.1), not that much of attention has been paid in estimating the number of components p.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Fisher, R. A. (1929). Tests of significance in harmonic Analysis. Proceedings of the Royal Society London Series A, 125, 54ā€“59.

    Google ScholarĀ 

  2. Quinn, B.G. (1986). Testing for the presence of sinusoidal components. Journal of Applied Probability, 23(A), 201ā€“210.

    Google ScholarĀ 

  3. Quinn, B. G., & Hannan, E. J. (2001). The estimation and tracking of frequency. New York: Cambridge University Press.

    BookĀ  MATHĀ  Google ScholarĀ 

  4. Rao, C. R. (1988). Some results in signal detection. In S. S. Gupta & J. O. Berger (Eds.), Decision theory and related topics IV (pp. 319ā€“332). New York: Springer.

    Google ScholarĀ 

  5. Kundu, D., & Kundu, R. (1995). Consistent estimates of super imposed exponential signals when observations are missing. Journal of Statistical Planning and Inference, 44, 205ā€“218.

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  6. Kundu, D., & Mitra, A. (1995). Consistent method of estimating the superimposed exponential signals. Scandinavian Journal of Statistics, 22, 73ā€“82.

    MathSciNetĀ  MATHĀ  Google ScholarĀ 

  7. Akaike, H. (1969). Fitting autoregressive models for prediction. Annals of the Institute of Statistical Mathematics, 21, 243ā€“247.

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  8. Akaike, H. (1970). Statistical predictor identification. Annals of the Institute of Statistical Mathematics, 22, 203ā€“217.

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  9. Schwartz, S. C. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461ā€“464.

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  10. Rissanen, J. (1978). Modeling by shortest data description. Automatica, 14, 465ā€“471.

    ArticleĀ  MATHĀ  Google ScholarĀ 

  11. Bai, Z. D., Krishnaiah, P. R., & Zhao, L. C. (1986). On the detection of the number of signals in the presence of white noise. Journal of Multivariate Analysis, 20, 1ā€“25.

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  12. Kundu, D. (1992). Detecting the number of signals for undamped exponential models using information theoretic criteria. Journal of Statistical Computation and Simulation, 44, 117ā€“131.

    ArticleĀ  Google ScholarĀ 

  13. Sakai, H. (1990). An application of a BIC-type method to harmonic analysis and a new criterion for order determination of an error process. IEEE Transaction of Acoustics Speech Signal Process, 38, 999ā€“1004.

    ArticleĀ  Google ScholarĀ 

  14. Quinn, B. G. (1989). Estimating the number of terms in a sinusoidal regression. Journal of Time Series Analysis, 10, 71ā€“75.

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  15. An, H.-Z., Chen, Z.-G., & Hannan, E. J. (1983). The maximum of the periodogram. Journal of Multivariate Analysis, 13, 383ā€“400.

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  16. Wang, X. (1993). An AIC type estimator for the number of cosinusoids. Journal of Time Series Analysis, 14, 433ā€“440.

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  17. Kavalieris, L., & Hannan, E. J. (1994). Determining the number of terms in a trigonometric regression. Journal of Time Series Analysis, 15, 613ā€“625.

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  18. Kundu, D. (1997). Estimating the number of sinusoids in additive white noise. Signal Processing, 56, 103ā€“110.

    ArticleĀ  MATHĀ  Google ScholarĀ 

  19. Kundu, D. (1998). Estimating the number of sinusoids and its performance analysis. Journal of Statistical Computation and Simulation, 60, 347ā€“362.

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

Ā© 2012 The Author(s)

About this chapter

Cite this chapter

Kundu, D., Nandi, S. (2012). Estimating the Number of Components. In: Statistical Signal Processing. SpringerBriefs in Statistics. Springer, India. https://doi.org/10.1007/978-81-322-0628-6_5

Download citation

Publish with us

Policies and ethics