identifiability {CopulaInference}

Identifiability of two-parameter copula families

Description

Determines if a copula family is identifiable with respect to the empirical margins. One-parameter copula families ("gaussian","gumbel","clayton","frank","plackett","joe") are identifiable whatever the margins. The rank of the gradient of the copula on the range of the margins is evaluated at 10000 parameter points within the lower and upper bounds of the copula family.

Usage

identifiability(data = NULL, family, rotation = 0, Fx = NULL, Fy = NULL)

Arguments

data

Matrix or data frame with 2 columns (X,Y). Can be pseudo-observations. If NULL, Fx and Fy must be provided.

family

Copula family: "gaussian", "t", "clayton", "frank", "gumbel", "joe", "plackett”, "bb1", "bb6", "bb7","bb8","ncs-gaussian", "ncs-clayton", "ncs-gumbel", "ncs-frank", "ncs-joe","ncs-plackett".

rotation

Rotation: 0 (default value), 90, 180, or 270.

Fx

Marginal cdf function applied to X (default is NULL).

Fy

Marginal cdf function applied to Y (default is NULL).

Value

out

True or False

References

Nasri & Remillard (2023). Identifiability and inference for copula-based semiparametric models for random vectors with arbitrary marginal distributions. arXiv 2301.13408.

Nasri (2020). On non-central squared copulas. Statistics and Probability Letters.

Examples

set.seed(1)
data = matrix(rpois(20,1),ncol=2)
out = identifiability(data,"gumbel")