Skip to main content
Log in

Global minima of least square cross validation for a symmetric polynomial kernel with finite support

  • Published:
Korean Journal of Computational & Applied Mathematics Aims and scope Submit manuscript

Abstract

The least squares cross validated bandwidth is the minimizer of the cross validation function for choosing the smooth parameter of a kernel density estimator. It is a completely automatic method, but it requires inordinate amounts of computational time. We present a convenient formula for calculation of the cross validation function when the kernel function is a symmetric polynomial with finite support. Also we suggest an algorithm for finding global minima of the cross validation function.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bowman, A. W.,An alternative method of cross validation for the smoothing of density estimates., Biometrika71 (1984), no. 2, 353–360.

    Article  MathSciNet  Google Scholar 

  2. Hall, P. and Marron, J. S.,Local minima in cross validation function, J. R. Statist. Soc. B.53 (1991), no. 1, 245–252.

    MATH  MathSciNet  Google Scholar 

  3. Lee, B. G. and Kim, B. C.,An efficient algorithm for the least-squares cross-validation with symmetric and polynomial kernels, Commun. Statist.-Simula.19 (1990), no. 4, 1513–1522.

    Article  MATH  Google Scholar 

  4. Park, B. U. and Marron, J. S.,Comparison of data-driven bandwidth selectors, Journ. of the Amer. Stat. Assoc.85 (1990), no. 409, 66–72.

    Article  Google Scholar 

  5. Rudemo, M.,Empirical choice of histograms and kernel density estimators, Scand. J. Statist.9 (1982), 65–78.

    MATH  MathSciNet  Google Scholar 

  6. Silverman, B. W.,Density Estimation for Statistics and Data Analysis, Chapman and Hall, 1986.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jung, KM., Kim, B.C. Global minima of least square cross validation for a symmetric polynomial kernel with finite support. Korean J. Com. & Appl. Math. 3, 183–192 (1996). https://doi.org/10.1007/BF03008900

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03008900

AMS Mathematics Subject Classification

Navigation