DDSE {capushe} R Documentation

## Model selection by Data-Driven Slope Estimation

### Description

DDSE is a model selection function based on the slope heuristics.

### Usage

DDSE(data, pct = 0.15, point = 0, psi.rlm = psi.bisquare, scoef = 2)


### 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. pct Minimum percentage of points for the plateau selection. It must be between 0 and 1. Default value is 0.15. point Minimum number of point for the plateau selection. If point is different from 0, pct is obsolete. psi.rlm Weight function used by rlm. psi.rlm="lm" for non robust linear regression. scoef Ratio parameter. Default value is 2.

### Details

Let M be the model collection and P=\{pen_{shape}(m),m\in M\}. The DDSE algorithm proceeds in four steps:

1. If several models in the collection have the same penalty shape value (column 2), only the model having the smallest contrast value \gamma_n(\hat{s}_m) (column 4) is considered.

2. For any p\in P, the slope \hat{\kappa}(p) (argument @kappa) of the linear regression (argument psi.rlm) on the couples of points \{(pen_{shape}(m),-\gamma_n (\hat{s}_m)); pen_{shape}(m)\geq p\} is computed.

3. For any p\in P, the model fulfilling the following condition is selected:

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

This gives an increasing sequence of change-points (p_i)_{1\leq i\leq I+1} (output @ModelHat$point_breaking). Let (N_i)_{1\leq i\leq I} (output @ModelHat$number_plateau) be the lengths of each "plateau".

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

capushe for a model selection function including AIC, BIC, the DDSE algorithm and the Djump algorithm. plot for graphical dsiplays of the DDSE algorithm and the Djump algorithm.
data(datacapushe)