Preface

During the last decades, semiparametric regression has become a popular flexible tool for specifying regression models. In this context, especially because computational power has tremendously increased, it is now possible to tackle complicated inferential problems, e.g., with Markov chain Monte Carlo simulation (MCMC), on virtually any modern computer. This script aims to cover the core knowledge of flexible regression models, frequentist and Bayesian estimation, computational details and software implementations. The script assumes a certain basic knowledge of the linear regression model and the generalized linear model (GLM).

The script is based on the following books:

  • Fahrmeir et al. (2013). Regression – Models, Methods and Applications.
  • Hastie, Tibshirani, and Friedman (2009). The Elements of Statistical Learning.
  • Ruppert, Wand, and Carrol (2003). Semiparametric Regression.
  • Wood (2006). Generalized Additive Models: An Introduction with R.

Moreover, the script is completely based on the statistical programming environment R. All packages used are freely available under the CRAN repository.

In addition, the data sets used in this script are freely available and can be downloaded from the following links.

References

Fahrmeir, Ludwig, Thomas Kneib, Stefan Lang, and Brian Marx. 2013. Regression – Models, Methods and Applications. Berlin: Springer-Verlag.

Hastie, T. J., R. J. Tibshirani, and J. Friedman. 2009. The Elements of Statistical Learning. 2nd ed. New York: Springer-Verlag. https://doi.org/10.1007/978-0-387-84858-7.

Ruppert, David, M. P. Wand, and R. J. Carrol. 2003. Semiparametric Regression. New York: Cambridge University Press. https://doi.org/10.1017/CBO9780511755453.

Simon, Thorsten. 2019. FlashAustria: Data and Model for Reanalyzing Flash Counts in Austria. https://R-Forge.R-project.org/projects/bayesr/.

Umlauf, Nikolaus, Daniel Adler, Thomas Kneib, Stefan Lang, and Achim Zeileis. 2015. “Structured Additive Regression Models: An R Interface to BayesX.” Journal of Statistical Software 63 (21): 1–46. https://doi.org/10.18637/jss.v063.i21.

Umlauf, Nikolaus, Nadja Klein, and Achim Zeileis. 2018. “BAMLSS: Bayesian Additive Models for Location, Scale, and Shape (and Beyond).” Journal of Computational and Graphical Statistics 27 (3). Taylor & Francis: 612–27. https://doi.org/10.1080/10618600.2017.1407325.

Umlauf, Nikolaus, Georg Mayr, Jakob Messner, and Achim Zeileis. 2012. “Why Does It Always Rain on Me? A Spatio-Temporal Analysis of Precipitation in Austria.” Austrian Journal of Statistics 41 (1): 81–92. https://doi.org/10.1002/joc.4913.

Wood, Simon N. 2006. Generalized Additive Models: An Introduction with R. Boca Raton: Chapman & Hall/CRC.