Djump: Model selection by dimension jump

In capushe: CAlibrating Penalities Using Slope HEuristics

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	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.
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=\sqrt{\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.

Details

The Djump algorithm proceeds in three steps:

1. For all \kappa>0, compute

   m(\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)}.

2. Find \hat{\kappa} such that C_{m(\hat{\kappa})} corresponds to the greatest jump of complexity if C_{tresh}=0 else \hat{\kappa} such that

   \hat{\kappa}=inf\{\kappa>0: C_{m(\kappa)}\leq C_{tresh}\}.

3. 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 model selected by the dimension jump method.
@ModelHat	A list describing the algorithm.
@ModelHat$jump	The vector of jump heights.
@ModelHat$kappa	The vector of the values of \kappa at each jump.
@ModelHat$model_hat	The vector of the selected models m(\kappa) by the jump.
@ModelHat$JumpMax	The location of the greatest jump.
@ModelHat$Kopt	\kappa_{opt}=scoef\hat{\kappa}.
@graph	A list computed for the plot method.

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)))

capushe documentation built on Nov. 27, 2023, 5:11 p.m.