Skip to main content

Part of the book series: Statistics and Computing ((SCO))

Abstract

A useful tool for examining the overall structure of data is kernel density estimation. It provides a graphical device for understanding the overall pattern of the data structure. This includes symmetry and the number and locations of modes and valleys. The basic idea is to redistribute the point mass at each datum point by a smoothed density centered at the datum point. An important question is how much the point mass should be smoothed out. This will be discussed in the next section. More detailed discussions on this subject can be found in Chapter 6.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Andrews, D.F., Herzberg, A.M. (1985). Data: A Collection of Problems from Many Fields for the Student and Research Worker, Springer Series in Statistics, Springer-Verlag, New York.

    Google Scholar 

  • Fan, J. (1992). Design-adaptive nonparametric regression, Journal of the American Statistical Association 87 (420): 998–1004.

    Article  MathSciNet  MATH  Google Scholar 

  • Fan, J. (1993). Local linear regression smoothers and their minimax efficiency, Annals of Statistics 21 (1): 196–216.

    Article  MathSciNet  MATH  Google Scholar 

  • Fan, J. and Gijbels, I. (1995a). Data-driven bandwidth selection in local polynomial fitting: Variable bandwidth and spatial adaptation, Journal of the Royal Statistical Society, Series B. To appear.

    Google Scholar 

  • Fan, J. and Gijbels, I. (1995b). Local Polynomial Modeling and Its Application—Theory and Methodologies, Chapman & Hall, New York.

    Google Scholar 

  • Flury, B. and Riedwyl, H. (1988). Multivariate Statistics, A Practical Approach, Cambridge University Press, New York.

    Google Scholar 

  • Härdle, W. (1990). Applied Nonparametric Regression, Econometric Society Monographs No. 19. Cambridge University Press, New York.

    Google Scholar 

  • Hastie. T.J. and Loader, C.R. (1993). Local regression: Automatic kernel carpentry (with discussion), Statistical Science 8 (2): 120–143.

    Article  Google Scholar 

  • Marron, J.S. and Nolan, D. (1918). Canonical kernels for density estimation, Statistics & Probability Utters 7 (3): 195–199.

    Article  MathSciNet  Google Scholar 

  • Projektgruppe “Das Sozio-ökonomische Panel” (1991). Das Sozio-öko-nomische Panel (SOEP) im Jahre. 1990/91, Deutsches Institut für Wirtschaftsforschung. Vierteljahreshefte zur Wirtschaftsforschung, pp. 146–155.

    Google Scholar 

  • Ruppert, D., Sheather, S.J. and Wand, M.P. (1996). An effective bandwidth selector for local least squares regression, Journal of the American Statistical Association. To appear.

    Google Scholar 

  • Ruppert, D. and Wand. M.P. (1994). Multivariate weighted least squares regression, Annals of Statistics. To appear.

    Google Scholar 

  • Scott, D.W. (1992). Multivariate Density Estimation: Theory, Practice, and Visualization, John Wiley & Sons, New York, Chichester.

    Google Scholar 

  • Silverman, B.W. (1986). Density Estimation for Statistics and Data. Analysis, Vol. 26 of Monographs on Statistics and Applied Probability, Chapman & Hall. London.

    Google Scholar 

  • Wand, M.P., Marron, J.S. and Ruppert, D. (1991). Transformations in density estimation (with discussion), Journal of the American Statistical Association 86 (414): 343–361.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Fan, J., Müller, M. (1995). Density and Regression Smoothing. In: XploRe: An Interactive Statistical Computing Environment. Statistics and Computing. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4214-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4214-7_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8699-8

  • Online ISBN: 978-1-4612-4214-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics