EstBiCop {CopulaInference}

Parameter estimation for bivariate copula-based models with arbitrary distributions

Description

Computes the estimation of the parameters of a copula-based model with arbitrary distributions, i.e, possibly mixtures of discrete and continuous distributions. Parametric margins are allowed. The estimation is based on a pseudo-likelihood adapted to ties.

Usage

EstBiCop(
  data = NULL,
  family,
  rotation = 0,
  Fx = NULL,
  Fxm = NULL,
  Fy = NULL,
  Fym = 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).

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).

Value

par

Copula parameters

family

Copula family

rotation

Rotation value

tauth

Kendall's tau corresponding to the estimated parameter

tauemp

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

rhoSth

Spearman's rho corresponding to the estimated parameter

rhoSemp

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

loglik

Log-likelihood

aic

Aic value

bic

Bic value

data

Matrix of values (could be (Fx,Fy))

F1

Cdf of X (Fx if provided, empirical otherwise)

F1m

Left-limit of F1 (Fxm if provided, empirical otherwise)

F2

Cdf of Y (Fy if provided, empirical otherwise)

F2m

Left-limit of F2 (Fym if provided, empirical otherwise)

ccdfx

Conditional cdf of X given Y and it left limit

ccdfxm

Left-limit of ccdfx

ccdfy

Conditional cdf of Y given X and it left limit

ccdfym

Left-limit of ccdfy

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(2)
data = matrix(rpois(20,1),ncol=2)
out0=EstBiCop(data,"gumbel")