Regression models for functional data, i.e., scalar-on-function, function-on-scalar and function-on-function regression models, are fitted by a component-wise gradient boosting algorithm.

This package is intended to fit regression models with functional variables. It is possible to fit models with functional response and/or functional covariates, resulting in scalar-on-function, function-on-scalar and function-on-function regression. Details on the functional regression models that can be fitted with FDboost can be found in Brockhaus et al. (2015, 2017, 2018) and Ruegamer et al. (2018). A hands-on tutorial for the package can be found in Brockhaus, Ruegamer and Greven (2017), see https://arxiv.org/abs/1705.10662.

Using component-wise gradient boosting as fitting procedure, FDboost relies on the R package mboost (Hothorn et al., 2017). A comprehensive tutorial to mboost is given in Hofner et al. (2014).

The main fitting function is `FDboost`

.
The model complexity is controlled by the number of boosting iterations (mstop).
Like the fitting procedures in mboost, the function `FDboost`

DOES NOT
select an appropriate stopping iteration. This must be chosen by the user.
The user can determine an adequate stopping iteration by resampling methods like
cross-validation or bootstrap.
This can be done using the function `applyFolds`

.

Brockhaus, S., Ruegamer, D. and Greven, S. (2017): Boosting Functional Regression Models with FDboost. <doi:10.18637/jss.v094.i10>

Brockhaus, S., Scheipl, F., Hothorn, T. and Greven, S. (2015): The functional linear array model. Statistical Modelling, 15(3), 279-300.

Brockhaus, S., Melcher, M., Leisch, F. and Greven, S. (2017): Boosting flexible functional regression models with a high number of functional historical effects, Statistics and Computing, 27(4), 913-926.

Brockhaus, S., Fuest, A., Mayr, A. and Greven, S. (2018): Signal regression models for location, scale and shape with an application to stock returns. Journal of the Royal Statistical Society: Series C (Applied Statistics), 67, 665-686.

Hothorn T., Buehlmann P., Kneib T., Schmid M., and Hofner B. (2017). mboost: Model-Based Boosting, R package version 2.8-1, https://cran.r-project.org/package=mboost

Hofner, B., Mayr, A., Robinzonov, N., Schmid, M. (2014). Model-based Boosting in R: A Hands-on Tutorial Using the R Package mboost. Computational Statistics, 29, 3-35. https://cran.r-project.org/package=mboost/vignettes/mboost_tutorial.pdf

Ruegamer D., Brockhaus, S., Gentsch K., Scherer, K., Greven, S. (2018). Boosting factor-specific functional historical models for the detection of synchronization in bioelectrical signals. Journal of the Royal Statistical Society: Series C (Applied Statistics), 67, 621-642.

`FDboost`

for the main fitting function and
`applyFolds`

for model tuning via resampling methods.