GofBiCop: Goodness-of-fit for bivariate copula-based models with...

In CopulaInference: Estimation and Goodness-of-Fit of Copula-Based Models with Arbitrary Distributions

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)

CopulaInference documentation built on April 21, 2023, 9:07 a.m.