Fitting bivariate MGL copula models for two continuous data

MGL.mle is used to fit bivariate copula regression models via maximum likelihood (ML) method for two continuous variables.

MGL.mle(
  U,
  copula = c("MGL", "MGL180", "MGL-EV", "MGL-EV180", "Gumbel", "Normal", "MGB2", "t"),
  hessian = TRUE,
  initpar,
  ...
)

Arguments

U

two-dimensional matrix with values in \([0,1]\).

copula

copula 'MGL', 'MGL180', "MGL-EV", "MGL-EV180", "MGB2", "Normal" , "t".

hessian

Logical. Should a numerically differentiated Hessian matrix be returned?

initpar

Initial values for the parameters to be optimized over.

...

additional arguments, see nlm for more details.

Value

A list containing the following components:

  • loglike: the value of the estimated maximum of the loglikelihood function.

  • copula: the name of the fitted copula. "MGL180" and "MGL-EV180" denote the survival MGL and MGL-EV copula respectively.

  • estimates: the point at which the maximum value of the loglikelihood is obtained.

  • se: the standard errors of the estimators.

  • AIC, BIC: the goodness fit of the regression models.

  • hessian: the hessian at the estimated maximum of the loglikelihood (if requested).

Details

The estimation method is performed via nlm function.

copula:

  • "MGB2" is multivariate GB2.

  • "Normal" and "t" denote the Gaussian copula and Student-t copula respectively.

  • "MGL" and "MGL-EV" denote the MGL and MGL-EV copula respectively.

  • "MGL180" and "MGL-EV180" denote the survival MGL and survival MGL-EV copula respectively.

  • "Gumbel" is Gumbel copula.

References

Zhang, F. Z. . "A generalized beta copula with applications in modeling multivariate long-tailed data." Insurance: Mathematics and Economics (2011).

Examples

  library(rMGLReg)
  Usim <- rcMGL.bivar(n = 500, pars = 0.5)
  m.MGL <- MGL.mle(Usim,
  copula  = "MGL",
  initpar = c(2))
  # estimation results
  m.MGL
#> $loglike
#> [1] 11.34389
#> 
#> $copula
#> $copula$name
#> [1] "MGL"
#> 
#> 
#> $estimates
#> [1] 0.4933301
#> 
#> $se
#> [1] 0.1149392
#> 
#> $hessian
#>           [,1]
#> [1,] -75.69433
#> 
#> $AIC
#> [1] -20.68779
#> 
#> $BIC
#> [1] -16.47318
#>