R: CAlibrating Penalities Using Slope HEuristics (CAPUSHE)

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 If `point` is different from 0, `pct` is obsolete.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.

Author(s)

Vincent Brault

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

data(datacapushe)
capushe(datacapushe) 
capushe(datacapushe,1000)

[Package capushe version 1.1.2 Index]