datacapushe {capushe} | R Documentation |

## datacapushe

### Description

A dataframe example for the `capushe package`

based on a simulated Gaussian
mixture dataset in `\R^3`

.

### Usage

`data(datacapushe)`

### Format

A data frame with 50 rows (models) and the following 4 variables:

`model`

a character vector

: model names.

`pen`

a numeric vector

: model penalty shape values.

`complexity`

a numeric vector

: model complexity values.

`contrast`

a numeric vector

: model contrast values.

### Details

The simulated dataset is composed of `n=1000`

observations in `\R^3`

. It
consists of an equiprobable mixture of three large "bubble" groups centered at
`\nu_1=(0,0,0)`

, `\nu_2=(6,0,0)`

and `\nu_3=(0,6,0)`

respectively. Each
bubble group `j`

is simulated from a mixture of seven components according
to the following density distribution:

`x\in\R^3\rightarrow 0.4\Phi(x|\mu_1+\nu_j,I_3)+\sum_{k=2}^70.1\Phi(x|\mu_k+\nu_j,0.1I_3)`

with `\mu_1=(0,0,0)`

, `\mu_2=(0,0,1.5)`

, `\mu_3=(0,1.5,0)`

, `\mu_4=(1.5,0,0,)`

,
`\mu_5=(0,0,-1.5)`

, `\mu_6=(0,-1.5,0)`

and `\mu_7=(-1.5,0,0,)`

. Thus the
distribution of the dataset is actually a `21`

-component Gaussian mixture.

A model collection of spherical Gaussian mixtures is considered and the dataframe
`datacapushe`

contains the maximum likelihood estimations for each of these models.
The number of free parameters of each model is used for the complexity values and `pen_{shape}`

is defined by this complexity divided by `n`

.

`datapartialcapushe`

and `datavalidcapushe`

can be used to run the
`validation`

function. `datapartialcapushe`

only
contains the models with less than `21`

components. `datavalidcapushe`

contains three models with `30`

, `40`

and `50`

components respectively.

### Source

http://www.math.univ-toulouse.fr/~maugis/CAPUSHE.html

### References

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

### Examples

```
data(datacapushe)
capushe(datacapushe,n=1000)
## BIC, DDSE and Djump all three select the true model
plot(capushe(datacapushe))
## Validation:
data(datapartialcapushe)
capushepartial=capushe(datapartialcapushe)
data(datavalidcapushe)
validation(capushepartial,datavalidcapushe) ## The slope heuristics should not
## be applied for datapartialcapushe.
```

*capushe*version 1.1.2 Index]