Scholary papers describing the methodology

The mboost package implements componentwise functional gradient descent boosting, originally invented by Bühlmann and Yu (2003). The theory and package are described in the review by Bühlmann and Hothorn (2007a), an overview about the implementation is given in Hothorn, Bühlmann, Kneib, Schmid, and Hofner (2010) and Hothorn and Bühlmann (2006). A tutorial can be found in Hofner, Mayr, Robinzonov, and Schmid (2014).

Boosting for generalised additive models with constraints is discussed in Hofner, Kneib, and Hothorn (2016). Unbiased model selection in generalised additive models is developed in Hofner, Hothorn, Kneib, and Schmid (2011).

Applications in survival analysis are described in Hothorn, Bühlmann, Dudoit, Molinaro, and van der Laan (2006), Schmid and Hothorn (2008b) and Mayr and Schmid (2014).

Geoadditive models have been dealt with by Kneib, Hothorn, and Tutz (2009), Hothorn, Müller, Schröder, Kneib, and Brandl (2011) and Schmid, Hothorn, Maloney, Weller, and Potapov (2011b), and, with special emphasis on monotonicity constraints, by Hofner, Müller, and Hothorn (2011b).

Boosted quantile regression models were introduced by Fenske, Kneib, and Hothorn (2011) and later extended to longitudinal data by Fenske, Fahrmeir, Hothorn, Rzehak, and Höhle (2013) and to the derivation of prediction intervals by Mayr, Hothorn, and Fenske (2012).

The application of P-spline base-learners was discussed by Schmid and Hothorn (2008a). Unbiased model selection was implemented as described by Hofner, Hothorn, Kneib, et al. (2011). An approach to non-linear time series can be found in Robinzonov, Tutz, and Hothorn (2012). Boosted classifiers based on a direct optimisation of the partial AUC were introduced by Schmid, Hothorn, Krause, and Rabe (2012).

Hothorn, Kneib, and Bühlmann (2014) used componentwise array boosting to fit a novel class of conditional transformation models; some simplifications are given by Möst, Schmid, Faschingbauer, and Hothorn (2016). In a similar spirit, Mayr, Fenske, Hofner, Kneib, and Schmid (2012) use the package to fit GAMLSS models.


[1] P. Bühlmann and B. Yu. “Boosting with L2 Loss: Regression and Classification”. In: Journal of the American Statistical Association 98.462 (2003), pp. 324-338.

[2] T. Hothorn and P. Bühlmann. “Model-based Boosting in High Dimensions”. In: Bioinformatics 22.22 (Nov. 2006), pp. 2828–2829. DOI: doi:10.1093/bioinformatics/btl462.

[3] T. Hothorn, P. Bühlmann, S. Dudoit, et al. “Survival Ensembles”. In: Biostatistics 7.3 (Jul. 2006), pp. 355–373. DOI: 10.1093/biostatistics/kxj011.

[4] P. Bühlmann and T. Hothorn. “Boosting Algorithms: Regularization, Prediction and Model Fitting”. In: Statistical Science 22.4 (2007). with discussion, pp. 477–505. DOI: 10.1214/07-STS242.

[5] M. Schmid and T. Hothorn. “Boosting Additive Models using Component-wise P-splines as Base-learners”. In: Computational Statistics & Data Analysis 53.2 (2008), pp. 298–311. DOI: 10.1016/j.csda.2008.09.009.

[6] M. Schmid and T. Hothorn. “Flexible Boosting of Accelerated Failure Time Models”. In: BMC Bioinformatics 9 (2008), p. 269. DOI: doi:10.1186/1471-2105-9-269. URL:

[7] T. Kneib, T. Hothorn and G. Tutz. “Variable Selection and Model Choice in Geoadditive Regression Models”. In: Biometrics 65.2 (2009), pp. 626–634. DOI: 10.1111/j.1541-0420.2008.01112.x.

[8] T. Hothorn, P. Bühlmann, T. Kneib, et al. “Model-based Boosting 2.0”. In: Journal of Machine Learning Research 11 (2010), pp. 2109–2113. URL:

[9] N. Fenske, T. Kneib and T. Hothorn. “Identifying Risk Factors for Severe Childhood Malnutrition by Boosting Additive Quantile Regression”. In: Journal of the American Statistical Association 106.494 (2011), pp. 494–510. DOI: 10.1198/jasa.2011.ap09272.

[10] B. Hofner, T. Hothorn, T. Kneib, et al. “A Framework for Unbiased Model Selection Based on Boosting”. In: Journal of Computational and Graphical Statistics 20.4 (2011), pp. 956–971. DOI: 10.1198/jcgs.2011.09220.

[11] B. Hofner, J. Müller and T. Hothorn. “Monotonicity-constrained Species Distribution Models”. In: Ecology 92.10 (2011), pp. 1895–1901. DOI: 10.1890/10-2276.1.

[12] T. Hothorn, J. Müller, B. Schröder, et al. “Decomposing Environmental, Spatial, and Spatiotemporal Components of Species Distributions”. In: Ecological Monographs 81 (2011), pp. 329–347. DOI: 10.1890/10-0602.1.

[13] M. Schmid, T. Hothorn, K. O. Maloney, et al. “Geoadditive Regression Modeling of Stream Biological Condition”. In: Environmental and Ecological Statistics 18.4 (2011), pp. 709–733. DOI: 10.1007/s10651-010-0158-4.

[14] A. Mayr, N. Fenske, B. Hofner, et al. “Generalized Additive Models for Location, Scale and Shape for High Dimensional Data-a Flexible Approach Based on Boosting: Boosting Generalized Additive Models for Location, Scale and Shape”. In: Journal of the Royal Statistical Society: Series C (Applied Statistics) 61.3 (2012), pp. 403–427. DOI: 10.1111/j.1467-9876.2011.01033.x.

[15] A. Mayr, T. Hothorn and N. Fenske. “Prediction Intervals for Future BMI Values of Individual Children–A Non-parametric Approach by Quantile Boosting”. In: BMC Medical Research Methodology 12 (2012), p. 6. DOI: 10.1186/1471-2288-12-6.

[16] N. Robinzonov, G. Tutz and T. Hothorn. “Boosting Techniques for Nonlinear Time Series Models”. In: AStA Advances in Statistical Analysis 96.1 (2012), pp. 99–122. DOI: 10.1007/s10182-011-0163-4.

[17] M. Schmid, T. Hothorn, F. Krause, et al. “A PAUC-based Estimation Technique for Disease Classification and Biomarker Selection”. In: Statistical Applications in Genetics and Molecular Biology 11.5 (2012). DOI: 10.1515/1544-6115.1792.

[18] N. Fenske, L. Fahrmeir, T. Hothorn, et al. “Boosting Structured Additive Quantile Regression for Longitudinal Childhood Obesity Data”. In: International Journal of Biostatistics 9.1 (2013). DOI: 10.1515/ijb-2012-0035.

[19] B. Hofner, A. Mayr, N. Robinzonov, et al. “Model-based Boosting in R: a Hands-on Tutorial Using the R Package Mboost”. In: Computational Statistics 29.1-2 (2014), pp. 3–35. DOI: 10.1007/s00180-012-0382-5.

[20] T. Hothorn, T. Kneib and P. Bühlmann. “Conditional Transformation Models”. In: Journal of the Royal Statistical Society: Series B (Statistical Methodology) 76.1 (2014), pp. 3–27. DOI: 10.1111/rssb.12017.

[21] A. Mayr and M. Schmid. “Boosting the Concordance Index for Survival Data – A Unified Framework To Derive and Evaluate Biomarker Combinations”. In: PLoS ONE 9.1 (2014), p. e84483. DOI: 10.1371/journal.pone.0084483.

[22] B. Hofner, T. Kneib and T. Hothorn. “A Unified Framework of Constrained Regression”. In: Statistics and Computing 26.1 (2016), pp. 1–14. DOI: 10.1007/s11222-014-9520-y.

[23] L. Möst, M. Schmid, F. Faschingbauer, et al. “Predicting Birth Weight with Conditionally Linear Transformation Models”. In: Statistical Methods in Medical Research 25.6 (2016), pp. 2781–2810. DOI: 10.1177/0962280214532745.