Skip to main content

Kader—An R Package for Nonparametric Kernel Adjusted Density Estimation and Regression

  • Chapter
  • First Online:
From Statistics to Mathematical Finance
  • 1432 Accesses

Abstract

In a series of three papers published from 2011 through 2013, Stute and coauthors introduced a fully data-adaptive nonparametric kernel method for pointwise univariate density estimation and likewise for regression estimation. For density estimation a robustified version of this adaptive method was also provided and the pointwise method was extended to an \(L_2\)-approach. Here, an R package is presented that implements (so far) parts of those methods. This package is a first attempt to narrow the gap between the theoretical derivation of the methods and their availability for practical applications.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /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 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
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

Similar content being viewed by others

References

  • Bowman, A.W., Azzalini, A.: sm: nonparametric smoothing methods. R package version 2.2-5.4 (2014). Available from http://www.stats.gla.ac.uk/~adrian/sm or http://azzalini.stat.unipd.it/Book_sm or https://CRAN.R-project.org/package=sm. Last accesses: November 2016.

  • Duong, T., Wand, M.: feature: Local Inferential Feature Significance for Multivariate Kernel Density Estimation. R package version 1.2.13. (2015). Available from https://CRAN.R-project.org/package=feature. Last access: November 2016.

  • Duong, T.: ks: Kernel Smoothing. R package version 1.10.4 (2016). Available from https://CRAN.R-project.org/package=ks. Last access: November 2016.

  • Eichner, G., Stute, W.: Kernel adjusted nonparametric regression. J. Stat. Plan. Infer. 142, 2537–2544 (2012) doi:10.1016/j.jspi.2012.03.011.

  • Eichner, G., Stute, W.: Rank transformations in kernel density estimation. J. Nonpar. Stat. 25, 427–445 (2013) doi:10.1080/10485252.2012.760737

  • Eichner, G., Stute, W.: Rank-Based Kernel Smoothing – \(L_2\)-approach. Talk presented at the 12\(^{th}\) Workshop on Stochastic Models, Statistics and Their Applications in Wroclaw, Poland, February 2015.

    Google Scholar 

  • Feluch, W., Koronacki, J.: A note on modified cross-validation in density estimation. Comput. Statist. Data Anal. 13, 143–151 (1992)

    Google Scholar 

  • Guidoum, A.C.: kedd: Kernel estimator and bandwidth selection for density and its derivatives.R package version 1.0.3 (2015). Available from http://CRAN.R-project.org/package=kedd. Last access: November 2016.

  • Härdle, W.: Applied nonparametric regression. Cambridge Univ. Press, Cambridge (1990)

    Google Scholar 

  • Hayfield, T., Racine, J.S.: Nonparametric Econometrics: The np Package. J. Stat. Software 27(5) (2008). http://www.jstatsoft.org/v27/i05

  • Herrmann, E., packaged for R and enhanced by Maechler, M.: lokern: Kernel Regression Smoothing with Local or Global Plug-in Bandwidth, R package version 1.1-8 (2016). Available from http://CRAN.R-project.org/package=lokern. Last access: February 16, 2017.

  • Nadaraya, E.A.: On estimating regression. Theory Prob. Appl. 10, 186–190 (1964)

    Google Scholar 

  • Parzen, E.: On the Estimation of a Probability Density Function and the Mode. Ann. Math. Statist. 33, 1065–1076 (1962)

    Google Scholar 

  • R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/. Last access: December 2016.

  • Rosenblatt, M.: Remarks on some Nonparametric Estimates of a Density Function. Ann. Math. Statist. 27 832–837 (1956)

    Google Scholar 

  • Sheather, S.J., Jones, M.C.: A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society series B, 53, 683–690 (1991)

    Google Scholar 

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

    Google Scholar 

  • Srihera, R., Stute, W.: Kernel Adjusted Density Estimation. Statistics Probability Letters 81, 571–579 (2011) doi:10.1016/j.spl.2011.01.013

  • Venables, W.N., Ripley, B.D.: Modern Applied Statistics with S. Springer New York (2002)

    Google Scholar 

  • Wand, M.: KernSmooth: Functions for Kernel Smoothing Supporting Wand & Jones (1995). R package version 2.23-15 (2015). Available from https://CRAN.R-project.org/package=KernSmooth. Last access: November 2016.

  • Wand, M.P., Jones, M.C.: Kernel Smoothing. Chapman & Hall, London (1995)

    Google Scholar 

  • Watson, G.S.: Smooth regression analysis. Sankhyā, Series A 26, 359–372 (1964)

    Google Scholar 

Download references

Acknowledgements

Thanks to the two referees whose constructive criticism and suggestions helped to improve the paper considerably.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gerrit Eichner .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Eichner, G. (2017). Kader—An R Package for Nonparametric Kernel Adjusted Density Estimation and Regression. In: Ferger, D., González Manteiga, W., Schmidt, T., Wang, JL. (eds) From Statistics to Mathematical Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-50986-0_15

Download citation

Publish with us

Policies and ethics