capushe {capushe} R Documentation

## CAlibrating Penalities Using Slope HEuristics (CAPUSHE)

### Description

The capushe function proposes two algorithms based on the slope heuristics to calibrate penalties in the context of model selection via penalization.

### Usage

capushe(data,n=0,pct=0.15,point=0,psi.rlm=psi.bisquare,scoef=2,
Careajump=0,Ctresh=0)


### Arguments

 data data is a matrix or a data.frame with four columns of the same length and each line corresponds to a model: The first column contains the model names. The second column contains the penalty shape values. The third column contains the model complexity values. The fourth column contains the minimum contrast value for each model. n n is the sample size. pct Minimum percentage of points for the plateau selection. See DDSE for more details. point Minimum number of point for the plateau selection (See DDSE for more details). If point is different from 0, pct is obsolete. psi.rlm Weight function used by rlm. See DDSE for more details. psi.rlm="lm" for non robust linear regression. scoef Ratio parameter. Default value is 2. Careajump Constant of jump area (See Djump for more details). Default value is 0 (no area). Ctresh Maximal treshold for the complexity associated to the penalty coefficient (See Djump for more details). Default value is 0 (Maximal jump selected as the greater jump).

### Details

The model \hat{m} selected by the procedure fulfills

\hat{m}= argmin \gamma_n (\hat{s}_m)+scoef\times \kappa\times pen_{shape}(m)

where

• \kappa is the penalty coefficient.

• \gamma_n is the empirical contrast.

• \hat{s}_m is the estimator for the model m.

• scoef is the ratio parameter.

• pen_{shape} is the penalty shape.

The capushe function calls the functions DDSE and Djump to calibrate \kappa, see the description of these functions for more details. In the case of equality between two penalty shape values, only the model with the smallest contrast is considered.

### Value

 @DDSE A list returned by the DDSE function. @DDSE@model The model selected by the DDSE function. @DDSE@kappa The vector of the successive slope values. @DDSE@ModelHat A list providing details about the model selected by the DDSE function. @DDSE@interval A list about the "slope interval" corresponding to the plateau selected in DDSE. See DDSE for more details. @DDSE@graph A list computed for the plot function. @Djump A list returned by the Djump function. @Djump@model The model selected by the Djump function. @Djump@ModelHat A list providing details about the model selected by the Djump function. @Djump@graph A list computed for the plot function. @AIC_capushe A list returned by the AICcapushe function. @BIC_capushe A list returned by the BICcapushe function. @n Sample size.

Vincent Brault

### References

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

Djump, DDSE, AIC or BIC to use only one of these model selection functions. plot for graphical displays of DDSE and Djump.
data(datacapushe)