Cort copulas

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
)

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.

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.

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.

References

laverny2020cort

Examples

(Cort(LifeCycleSavings[,1:3]))
#> Splitting...
#> 
#>      1 leaves to split...
#>      5 leaves to split...
#>      10 leaves to split...
#>      4 leaves to split...
#>      3 leaves to split...
#> Enforcing constraints...
#> Done !
#> Cort copula model: 50x3-dataset and 116 leaves.