Cort-Class {cort} R Documentation

## Cort copulas

Cort class

### Usage

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
)


### Arguments

 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.

### Details

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.

### Value

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.

### References

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

### Examples

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


[Package cort version 0.3.2 Index]