EllCopLikelihood {ElliptCopulas} | R Documentation |
Computes the likelihood
\frac{g(Q_g(U) \Sigma^{-1} Q_g(U))}{f_g(Q_g(U_1)) \cdots f_g(Q_g(U_d))}
for a vector (U_1, \dots, U_d)
on the unit cube
and for a d
-dimensional generator g
whose univariate density and quantile functions
are respectively f_g
and Q_g
.
This is to the likelihood of the copula associated with the elliptical distribution
having density |det(\Sigma)|^{-1/2} g(x \Sigma^{-1} x)
.
EllCopLikelihood(grid, g_d, pointsToCompute, Sigma_m1, log = TRUE)
grid |
the discretization grid on which the generator is given. |
g_d |
the values of the |
pointsToCompute |
the points |
Sigma_m1 |
the inverse correlation matrix of the elliptical distribution. |
log |
if |
a vector (of length 1 if pointsToCompute
is a vector) of likelihoods
associated with each observation.
Derumigny, A., & Fermanian, J. D. (2022). Identifiability and estimation of meta-elliptical copula generators. Journal of Multivariate Analysis, article 104962. doi:10.1016/j.jmva.2022.104962.
EllCopEst
for the estimation of elliptical copula,
EllCopEst
for the estimation of elliptical copula.
grid = seq(0,50,by = 0.01)
gdnorm = DensityGenerator.normalize(grid = grid, grid_g = exp(-grid/2), d = 3)
gdnorm2 = DensityGenerator.normalize(grid = grid, grid_g = 1/(1+grid^2), d = 3)
X = EllCopSim(n = 30, d = 3, grid = grid, g_d = gdnorm)
logLik = EllCopLikelihood(grid , g_d = gdnorm , X,
Sigma_m1 = diag(3), log = TRUE)
logLik2 = EllCopLikelihood(grid , g_d = gdnorm2 , X,
Sigma_m1 = diag(3), log = TRUE)
print(c(sum(logLik), sum(logLik2)))