GofBiCop {CopulaInference}

Goodness-of-fit for bivariate copula-based models with arbitrary distributions

Description

Goodness-of-fit tests for copula-based models for data with arbitrary distributions. The tests statistics are the Cramer-von Mises statistic (Sn), the difference between the empirical Kendall's tau and the theoretical one, and the difference between the empirical Spearman's rho and the theoretical one.

Usage

GofBiCop(
  data = NULL,
  family,
  rotation = 0,
  Fx = NULL,
  Fxm = NULL,
  Fy = NULL,
  Fym = NULL,
  B = 100,
  n_cores = 1
)

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).

Fxm

left limit of marginal cdf function applied to X default is NULL).

Fy

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

Fym

left limit of marginal cdf function applied to Y (default is NULL).

B

Number of bootstrap samples (default 100)

n_cores

Number of cores to be used for parallel computing (default is 1).

Value

pvalueSn

Pvalue of Sn in percent

pvalueTn

Pvalue of Tn in percent

pvalueRn

Pvalue of Rn in percent

Sn

Value of Cramer-von Mises statistic Sn

Tn

Value of Kendall's statistic Tn

Rn

Value of Spearman's statistic Rn

cpar

Copula parameters

family

Copula family

rotation

Rotation value

tauth

Kendall's tau (from the multilinear theoretical copula)

tauemp

Empirical Kendall's tau (from the multilinear empirical copula)

rhoth

Spearman's rho (from the multilinear theoretical copula)

rhoemp

Empirical Spearman's rho (from the multilinear empirical copula)

parB

Bootstrapped parameters

loglik

Log-likelihood

aic

AIC value

bic

BIC value

References

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

Nasri & Remillard (2023). Goodness-of-fit and bootstrapping for copula-based random vectors with arbitrary marginal distributions.

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

Examples

data = rvinecopulib::rbicop(10,"gumbel",rotation=0,2)
out=GofBiCop(data,family="gumbel",B=10)