Djump {capushe} | R Documentation |
Model selection by dimension jump
Description
Djump
is a model selection function based on the slope heuristics.
Usage
Djump(data,scoef=2,Careajump=0,Ctresh=0)
Arguments
data |
|
scoef |
Ratio parameter. Default value is 2. |
Careajump |
Constant of jump area. Default value is 0 (no area). In practice,
it is advisable to take |
Ctresh |
Maximal treshold for the complexity associated to the penalty coefficient.
Default value is 0 (Maximal jump selected as the greatest jump). In practice,
it is advisable to take |
Details
The Djump algorithm proceeds in three steps:
For all
\kappa>0
, computem(\kappa)\in argmin_{m\in M} \{\gamma_n(\hat{s}_m)+\kappa\times pen_{shape}(m)\}
This gives a decreasing step function
\kappa \mapsto C_{m(\kappa)}
.Find
\hat{\kappa}
such thatC_{m(\hat{\kappa})}
corresponds to the greatest jump of complexity ifC_{tresh}=0
else\hat{\kappa}
such that\hat{\kappa}=inf\{\kappa>0: C_{m(\kappa)}\leq C_{tresh}\}.
Select
\hat{m}=m(scoef\times\hat{\kappa})
(output@model
).
Arlot has proposed a jump area containing the maximal jump defined by :
[\kappa(1-Careajump);\kappa(1+Careajump)].
If Careajump>0
, Djump
return the area with the greatest jump. In practice,
it is advisable to take Careajump=\frac{log(n)}{n}
where n
is the number of observations.
Value
@model |
The |
@ModelHat |
A list describing the algorithm. |
@ModelHat$jump |
The vector of jump heights. |
@ModelHat$kappa |
The vector of the values of |
@ModelHat$model_hat |
The vector of the selected models |
@ModelHat$JumpMax |
The location of the greatest jump. |
@ModelHat$Kopt |
|
@graph |
A list computed for the |
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
See Also
capushe
for a model selection function including AIC
,
BIC
, the DDSE
algorithm and the Djump
algorithm. plot
for a graphical display of the DDSE
algorithm and the Djump
algorithm.
Examples
data(datacapushe)
Djump(datacapushe)
plot(Djump(datacapushe))
Djump(datacapushe,Careajump=sqrt(log(1000)/1000))
plot(Djump(datacapushe,Careajump=sqrt(log(1000)/1000)))
Djump(datacapushe,Ctresh=1000/log(1000))
plot(Djump(datacapushe,Ctresh=1000/log(1000)))