DDSE {capushe} | R Documentation |
DDSE
is a model selection function based on the slope heuristics.
DDSE(data, pct = 0.15, point = 0, psi.rlm = psi.bisquare, scoef = 2)
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. |
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 γ_n(\hat{s}_m) (column 4) is considered.
For any p\in P, the slope \hat{κ}(p) (argument @kappa
) of the linear regression
(argument psi.rlm
) on the couples of points \{(pen_{shape}(m),-γ_n (\hat{s}_m)); pen_{shape}(m)≥q p\}
is computed.
For any p\in P, the model fulfilling the following condition is selected:
\hat{m}(p)= argmin γ_n (\hat{s}_m)+scoef\times \hat{κ}(p)\times pen_{shape}(m).
This gives an increasing sequence of change-points (p_i)_{1≤q i≤q I+1} (output
@ModelHat$point_breaking
). Let (N_i)_{1≤q i≤q I} (output @ModelHat$number_plateau
)
be the lengths of each "plateau".
If point
is different from 0, let \hat{i}= max
\{1≤q i≤q I; N_i≥q point\} else let \hat{i}= max
\{1≤q i≤q I; N_i≥q pct∑_{l=1}^IN_l\} (output @ModelHat$imax
).
The model \hat{m}(p_{\hat{i}}) (output @model
) is finally returned.
The "slope interval" is the interval [a,b] where a=inf\{\hat{κ}(p),p\in[p_{\hat{i}},p_{\hat{i}+1}[\cap P\} and b=sup\{\hat{κ}(p),p\in[p_{\hat{i}},p_{\hat{i}+1}[\cap P\}.
@model |
The |
@kappa |
The vector of the successive slope values. |
@ModelHat |
A list describing the algorithm. |
@ModelHat$model_hat |
The vector of preselected models \hat{m}(p). |
@ModelHat$point_breaking |
The vector of the breaking points (p_i)_{1≤q i≤q I+1}. |
@ModelHat$number_plateau |
The vector of the lengths (N_i)_{1≤q i≤q I}. |
@ModelHat$imax |
The rank \hat{i} of the selected plateau. |
@interval |
A list about the "slope interval". |
@interval$interval |
The slope interval. |
@interval$percent_of_points |
The proportion N_{\hat{i}}/∑_{l=1}^IN_l. |
@graph |
A list computed for the |
Vincent Brault
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
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) DDSE(datacapushe) plot(DDSE(datacapushe)) ## DDSE with "lm" for the regression DDSE(datacapushe,psi.rlm="lm")