DDSE {capushe}  R Documentation 
Model selection by DataDriven 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 

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 
psi.rlm 
Weight function used by 
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:
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.For any
p\in P
, the slope\hat{\kappa}(p)
(argument@kappa
) of the linear regression (argumentpsi.rlm
) on the couples of points\{(pen_{shape}(m),\gamma_n (\hat{s}_m)); pen_{shape}(m)\geq p\}
is computed.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 changepoints
(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".If
point
is different from 0, let\hat{i}=
max\{1\leq i\leq I; N_i\geq point\}
else let\hat{i}=
max\{1\leq i\leq I; N_i\geq pct\sum_{l=1}^IN_l\}
(output@ModelHat$imax
). The model\hat{m}(p_{\hat{i}})
(output@model
) is finally returned.
The "slope interval" is the interval [a,b]
where a=inf\{\hat{\kappa}(p),p\in[p_{\hat{i}},p_{\hat{i}+1}[\cap P\}
and b=sup\{\hat{\kappa}(p),p\in[p_{\hat{i}},p_{\hat{i}+1}[\cap P\}
.
Value
@model 
The 
@kappa 
The vector of the successive slope values. 
@ModelHat 
A list describing the algorithm. 
@ModelHat$model_hat 
The vector of preselected models 
@ModelHat$point_breaking 
The vector of the breaking points 
@ModelHat$number_plateau 
The vector of the lengths 
@ModelHat$imax 
The rank 
@interval 
A list about the "slope interval". 
@interval$interval 
The slope interval. 
@interval$percent_of_points 
The proportion 
@graph 
A list computed for the 
Author(s)
Vincent Brault
References
http://www.math.univtoulouse.fr/~maugis/CAPUSHE.html
http://www.math.upsud.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/ s1122201192361
See Also
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.
Examples
data(datacapushe)
DDSE(datacapushe)
plot(DDSE(datacapushe))
## DDSE with "lm" for the regression
DDSE(datacapushe,psi.rlm="lm")