Preface

Welcome

Welcome to the notes for Nonparametric Statistics. The course is part of the MSc in Statistics for Data Science from Carlos III University of Madrid.

The course is designed to have, roughly, one session per each main topic in the syllabus. The schedule is tight due to time constraints, which will inevitably make the treatment of certain methods somewhat superficial. Nevertheless, the course will hopefully give you a respectable panoramic view of the different available topics in nonparametric statistics. A broad view of the syllabus is:

  1. Introduction
  2. Kernel density estimation I
  3. Kernel density estimation II
  4. Kernel regression estimation I
  5. Kernel regression estimation II
  6. Nonparametric tests

Main references and credits

Several great reference books have been used for preparing these notes. The following list presents the books that have been consulted:

These notes are possible due to the existence of the incredible pieces of software by Xie (2016), Xie (2020), Allaire et al. (2020), Xie and Allaire (2020), and R Core Team (2020). Also, certain hacks to improve the design layout have been possible due to the outstanding work by Úcar (2018). The icons used in the notes were designed by madebyoliver, freepik, and roundicons from Flaticon.

Last but not least, the notes have benefited from contributions from the following people (alphabetical ordering):

Contributions

Contributions, reporting of typos, and feedback on the notes are very welcome. Just send an email to and give me a good reason for writing your name in the list of contributors!

License

All the material in these notes is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Public License (CC BY-NC-ND 4.0). You may not use this material except in compliance with the aforementioned license. The human-readable summary of the license states that:

  • You are free to:
    • Share – Copy and redistribute the material in any medium or format.
  • Under the following terms:
    • Attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
    • NonCommercial – You may not use the material for commercial purposes.
    • NoDerivatives – If you remix, transform, or build upon the material, you may not distribute the modified material.

Citation

You may use the following \(\mathrm{B{\scriptstyle{IB}} \! T\!_{\displaystyle E} \! X}\) entry when citing these notes:

@book{Garcia-Portugues2026,
    title        = {Notes for Nonparametric Statistics},
    author       = {Garc\'ia-Portugu\'es, E.},
    year         = {2026},
    note         = {Version 6.13.3. ISBN 978-84-09-29537-1},
    url          = {https://egarpor.github.io/NP-UC3M/}
}

You may also want to use the following template:

García-Portugués, E. (2026). Notes for Nonparametric Statistics. Version 6.13.3. ISBN 978-84-09-29537-1. Available at https://egarpor.github.io/NP-UC3M/.

References

Allaire, J. J., Y. Xie, J. McPherson, J. Luraschi, K. Ushey, A. Atkins, H. Wickham, J. Cheng, W. Chang, and R. Iannone. 2020. rmarkdown: Dynamic Documents for R. https://github.com/rstudio/rmarkdown.
Chacón, J. E., and T. Duong. 2018. Multivariate Kernel Smoothing and Its Applications. Vol. 160. Monographs on Statistics and Applied Probability. Boca Raton: CRC Press. https://doi.org/10.1201/9780429485572.
D’Agostino, R. B., and M. A. Stephens, eds. 1986. Goodness-of-Fit Techniques. Vol. 68. Statistics: Textbooks and Monographs. New York: Marcel Dekker. https://www.routledge.com/Goodness-of-Fit-Techniques/DAgostino/p/book/9780367580346.
DasGupta, A. 2008. Asymptotic Theory of Statistics and Probability. Springer Texts in Statistics. New York: Springer. https://doi.org/10.1007/978-0-387-75971-5.
Fan, J., and I. Gijbels. 1996. Local Polynomial Modelling and Its Applications. Vol. 66. Monographs on Statistics and Applied Probability. London: Chapman & Hall. https://doi.org/10.1201/9780203748725.
Li, Q., and J. S. Racine. 2007. Nonparametric Econometrics. Princeton: Princeton University Press. https://press.princeton.edu/books/hardcover/9780691121611/nonparametric-econometrics.
Loader, C. 1999. Local Regression and Likelihood. Statistics and Computing. New York: Springer. https://doi.org/10.2307/1270956.
Nelsen, R. B. 2006. An Introduction to Copulas. Second. Springer Series in Statistics. New York: Springer-Verlag. https://doi.org/10.1007/0-387-28678-0.
R Core Team. 2020. R: A Language and Environment for Statistical Computing. Vienna. https://www.R-project.org/.
Scott, D. W. 2015. Multivariate Density Estimation. Second. Wiley Series in Probability and Statistics. Hoboken: John Wiley & Sons. https://doi.org/10.1002/9781118575574.
Sheskin, D. J. 2011. Handbook of Parametric and Nonparametric Statistical Procedures. Fifth. Boca Raton: CRC Press. https://doi.org/10.1201/9780429186196.
Silverman, B. W. 1986. Density Estimation for Statistics and Data Analysis. Monographs on Statistics and Applied Probability. London: Chapman & Hall. https://doi.org/10.1007/978-1-4899-3324-9.
Úcar, I. 2018. “Energy Efficiency in Wireless Communications for Mobile User Devices.” PhD thesis, Universidad Carlos III de Madrid. https://enchufa2.github.io/thesis/.
van der Vaart, A. W. 1998. Asymptotic Statistics. Vol. 3. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511802256.
Wand, M. P., and M. C. Jones. 1995. Kernel Smoothing. Vol. 60. Monographs on Statistics and Applied Probability. London: Chapman & Hall. https://doi.org/10.1201/b14876.
Wasserman, L. 2004. All of Statistics. Springer Texts in Statistics. New York: Springer. https://doi.org/10.1007/978-0-387-21736-9.
———. 2006. All of Nonparametric Statistics. Springer Texts in Statistics. New York: Springer. https://doi.org/10.1007/0-387-30623-4.
Xie, Y. 2016. Bookdown: Authoring Books and Technical Documents with R Markdown. The r Series. Boca Raton: CRC Press. https://bookdown.org/yihui/bookdown/.
———. 2020. knitr: A General-Purpose Package for Dynamic Report Generation in R. https://CRAN.R-project.org/package=knitr.
Xie, Y., and J. J. Allaire. 2020. tufte: Tufte’s Styles for R Markdown Documents. https://CRAN.R-project.org/package=tufte.