capushe-package: Capushe

Description

This package includes functions for model selection via penalization. The model selection criterion has the following form: \(\gamma_n (\hat{s}_m)+scoef\times\kappa\times pen_{shape}(m)\). Two algorithms based on the slope heuristics are proposed to calibrate the parameter \(\kappa\) in the penalty: the data-driven slope estimation algorithm (DDSE) and the dimension jump algorithm (Djump).

Arguments

Author

Sylvain Arlot, Vincent Brault, Jean-Patrick Baudry, Cathy Maugis and Bertrand Michel.

Maintainer: Vincent Brault <vincent.brault@math.u-psud.fr>

Details

The data-driven slope estimation algorithm and the dimension jump algorithm are respectively implemented into the DDSE function and the Djump function. Somes classes are defined for the outputs of DDSE and Djump and a graphical display is available for each one of these two classes. DDSE and Djump are both included in the capushe function which is the main function of the package.

References

http://www.math.univ-toulouse.fr/~maugis/CAPUSHE.html

http://www.math.u-psud.fr/~brault/capushe.html

Article: Baudry, J.-P., Maugis, C. and Michel, B. (2011) Slope heuristics: overview and implementation. Statistics and Computing, to appear. doi: 10.1007/ s11222-011-9236-1

Examples

Run this code

data(datacapushe)
## capushe returns the same model with DDSE and Djump:
capushe(datacapushe)
## capushe also returns the model selected by AIC and BIC
capushe(datacapushe,n=1000)
## Djump only
Djump(datacapushe)
## DDSE only
DDSE(datacapushe)
## Graphical representations
plot(Djump(datacapushe))
plot(DDSE(datacapushe))
plot(capushe(datacapushe))
## Validation procedure
data(datapartialcapushe)
capushepartial=capushe(datapartialcapushe)
plot(capushepartial)
## Additional data
data(datavalidcapushe)
validation(capushepartial,datavalidcapushe) ## The slope heuristics should not 
## be applied for datapartialcapushe.