Djump {capushe} | R Documentation |
Djump
is a model selection function based on the slope heuristics.
Djump(data,scoef=2,Careajump=0,Ctresh=0)
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 Careajump=√{\frac{log(n)}{n}} where n is the number of observations. |
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 Ctresh=\frac{n}{log(n)} where n is the number of observations. |
The Djump algorithm proceeds in three steps:
For all κ>0, compute
m(κ)\in argmin_{m\in M} \{γ_n(\hat{s}_m)+κ\times pen_{shape}(m)\}
This gives a decreasing step function κ \mapsto C_{m(κ)}.
Find \hat{κ} such that C_{m(\hat{κ})} corresponds to the greatest jump of complexity if C_{tresh}=0 else \hat{κ} such that
\hat{κ}=inf\{κ>0: C_{m(κ)}≤q C_{tresh}\}.
Select \hat{m}=m(scoef\times\hat{κ}) (output @model
).
Arlot has proposed a jump area containing the maximal jump defined by :
[κ(1-Careajump);κ(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.
@model |
The |
@ModelHat |
A list describing the algorithm. |
@ModelHat$jump |
The vector of jump heights. |
@ModelHat$kappa |
The vector of the values of κ at each jump. |
@ModelHat$model_hat |
The vector of the selected models m(κ) by the jump. |
@ModelHat$JumpMax |
The location of the greatest jump. |
@ModelHat$Kopt |
κ_{opt}=scoef\hat{κ}. |
@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 a graphical display of the DDSE
algorithm and the Djump
algorithm.
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)))