Cort-Class: Cort copulas
In cort: Some Empiric and Nonparametric Copula Models

Description Usage Arguments Details Value References Examples

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 :