satdad (version 1.1)

ecEmp: Empirical Extremal coefficients.

Description

Computes on a sample the extremal coefficients associated with threshold k.

Usage

ecEmp(sample, ind = 2, k, norm = TRUE)

Value

The function returns a list of two elements:

• subsets A list of subsets from \(\{1,...,d\}\).

  When ind is given as an integer, subsets is the list of subsets from \(\{1,...,d\}\) with cardinality ind. When ind is the list, it corresponds to subsets.

  When ind = "with.singletons" subsets is the list of all non empty subsets in \(\{1,...,d\}\).

  When ind = "all" subsets is the list of all subsets in \(\{1,...,d\}\) with cardinality larger or equal to 2.

• ec A vector of empirical extremal coefficients.

  An empirical extremal coefficient associated with the subset \(I\) is \(\hat{\ell}_{k,n}(1_I,0_{I^c})\). Its value lies in \((1, |I|)\).

  When norm = TRUE, then inverse normalized empirical ec are computed by \(1 - \dfrac{\hat{\ell}_{k,n}(1_I,0_{I^c})}{|I|}\).

Arguments

sample

A (n times d) matrix.

ind

A character string among "with.singletons" and "all" (without singletons), or an integer in \(\{2,...,d\}\) or a list of subsets from \(\{1,...,d\}\). The default is ind = 2, all pairwise coefficients are computed.

k

An integer smaller or equal to n.

norm

A boolean. `FALSE` (the default): empirical ec is computed. `TRUE`: inverse normalized empirical ec is computed.

Author

Cécile Mercadier ([e-mail])

See Also

ec, ellEmp, graphsEmp

Examples

## We produce below a figure on the dataset used in Mercadier  and Roustant (2019).

data(France)

ec_ymt <- ecEmp(sample = France$ymt, ind = 2, k = 25)

## The 9 largest inverse empirical pairwise extremal coefficients.
 graphsMapEmp(France$ymt, region='france', coord=France$coord, k=25, which="iecgraph", select=9)

## The 30 largest inverse empirical pairwise extremal coefficients.
graphsMapEmp(France$ymt, region='france', coord=France$coord, k=25, which="iecgraph", select=30)

## All the inverse empirical pairwise extremal coefficients.
graphsMapEmp(France$ymt, region='france', coord=France$coord, k=25, which="iecgraph")