Skip to main content
SpringerLink
Log in

Clustering Effect on the Statistical Estimation Accuracy of Distribution Density

  • Published:
Acta Applicandae Mathematicae Aims and scope Submit manuscript

Abstract

The paper is devoted to statistical nonparametric estimation of multivariate distribution density. The influence of data pre-clustering on the estimation accuracy of multimodal density is analyzed by means of the Monte Carlo method. It is shown that the soft clustering is more advantageous than the hard one. While a moderate increase in the number of clusters also increases the calculation time, it considerably reduces the estimation error.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aburdene, M.F.: Recursive computation of discrete Legendre polynomial coefficients. Multidimens. Syst. Signal Process. 7(2), 221–224 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ćwik, J., Koronacki, J.: Multivariate density estimation: a comparative study. Neural Comput. Appl. 6(3), 173–185 (1997)

    Article  Google Scholar 

  3. Duong, T.: Bandwidth matrices for multivariate kernel density estimation. PhD thesis (2004), p. 161

  4. Friedman, J.H.: Exploratory projection pursuit. J. Am. Stat. Assoc. 82(397), 249–266 (1987)

    Article  MATH  Google Scholar 

  5. Friedman, J.H., Stuetzle, W., Schroeder, A.: Projection pursuit density estimation. J. Am. Stat. Assoc. 79, 599–608 (1984)

    Article  MathSciNet  Google Scholar 

  6. Hall, P.: The Bootstrap and Edgeworth Expansion. Springer, New York (1992)

    Google Scholar 

  7. Huber, P.J.: Projection pursuit. Ann. Stat. 13(2), 435–475 (1985)

    MATH  MathSciNet  Google Scholar 

  8. Hwang, J.N., Lay, S.R., Lippman, A.: Nonparametric multivariate density estimation: a comparative study. IEEE Trans. Signal Process. 42(10), 2795–2810 (1994)

    Article  Google Scholar 

  9. Jeon, B., Landgrebe, D.A.: Fast parzen density estimation using clustering-based branch and bound. IEEE Trans. Pattern Anal. Mach. Intell. 16(9), 950–954 (1994)

    Article  Google Scholar 

  10. Jones, M.C., Marron, J.S., Sheather, S.J.: A brief survey of bandwidth selection for density estimation. J. Am. Stat. Assoc. 91, 401–407 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  11. Rudzkis, R., Radavičius, M.: Statistical estimations of a mixture of gaussian distributions. Acta Appl. Math. 38, 37–54 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ruzgas, T., Rudzkis, R., Kavaliauskas, M.: Application of clustering in the non-parametric estimation of distribution density. Nonlinear Anal. Model. Control 11(4), 393–411 (2006)

    Google Scholar 

  13. Scott, D.W.: Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley, New York (1992)

    MATH  Google Scholar 

  14. Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, London (1986)

    MATH  Google Scholar 

  15. Stone, C.J., Hansen, M., Kooperberg, C., Truong, Y.K.: Polynomial splines and their tensor products in extended linear modeling. Ann. Stat. 25, 1371–1470 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Wong, M.: A bootstrap testing procedure for investigating the number of subpopulations. J. Stat. Comput. Simul. 22, 99–112 (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Akademijos 4, 08663, Vilnius, Lithuania

    Rimantas Rudzkis & Tomas Ruzgas

Authors
  1. Rimantas Rudzkis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tomas Ruzgas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rimantas Rudzkis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rudzkis, R., Ruzgas, T. Clustering Effect on the Statistical Estimation Accuracy of Distribution Density. Acta Appl Math 97, 211–219 (2007). https://doi.org/10.1007/s10440-007-9127-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10440-007-9127-9

Keywords

Search

Navigation