Cort-Class {cort} | R Documentation |

Cort class

```
Cort(
x,
p_value_for_dim_red = 0.75,
min_node_size = 1,
pseudo_data = FALSE,
number_max_dim = NULL,
verbose_lvl = 1,
slsqp_options = NULL,
osqp_options = NULL,
N = 999,
force_grid = FALSE
)
```

`x` |
The data, must be provided as a matrix with each row as an observation. |

`p_value_for_dim_red` |
a p_value for the localized dimension reduction test |

`min_node_size` |
The minimum number of observation available in a leaf to initialize a split. |

`pseudo_data` |
set to True if you are already providing data on the copula space. |

`number_max_dim` |
The maximum number of dimension a split occurs in. Defaults to be all of the dimensions. |

`verbose_lvl` |
numeric. set the verbosity. 0 for no output and bigger you set it the most output you get. |

`slsqp_options` |
options for nloptr::slsqp to find breakpoints : you can change defaults. |

`osqp_options` |
options for the weights optimization. You can pass a call to osqp::osqpSettings, or NULL for defaults. |

`N` |
The number of bootstrap samples for p_values computations. |

`force_grid` |
Set to TRUE to force breakpoints to be on the n-checkerboard grid. |

This class implements the CORT algorithm to a fit a multivariate copula using piece constant density. Given a dataset `x`

, the function will produce an estimator for the copula of this dataset
that is tree-shaped, by recursive partitioning of the unit hypercube. the `min_node_size`

parameter controls the stopping conditions for the splitting procedure. Once the space is splitted,
we ran a quadratic solver, which options can be tweaked via the `osqp_options`

parameter, to ensure that the weights respect the copula conditions.

Once the model is fitted, it can be used through the classical (r/d/p/v)Copula functions to compute, respectively, random number generations, the density, the cdf and the volume function of the copula.

See O. Laverny, E. Masiello, V. Maume-Deschamps and D. Rullière (2020) for the details of this density estimation procedure, and `vignettes(package='cort')`

for examples of usecases.

An instance of the `Cort`

S4 class. The object represent the fitted copula and can be used through several methods to query classical (r/d/p/v)Copula methods, constraint influence, etc.
Beside returning some inputted parameters, notable slots are :

`data`

Your original data`dim`

The dimension of problem, number of columns of your dataset`f`

The empirical frequency in the leaves`p`

The fitted probabilities of each leaf`a`

Minimum points of leaves`b`

Maximum points of leaves`vols`

Volume of the leaves

More details about these slots can be found in the reference.

Laverny O, Maume-Deschamps V, Masiello E, RulliÃ¨re D (2020).
“Dependence Structure Estimation Using Copula Recursive Trees.”
*arXiv preprint arXiv:2005.02912*.

```
(Cort(LifeCycleSavings[,1:3]))
```

[Package *cort* version 0.3.2 Index]