View source: R/MarshallOlkin.R
BiCopEst.MO | R Documentation |
Estimation of Marshall-Olkin copulas
BiCopEst.MO( u1, u2, method, par.start = 0.5, kernel = "gaussian.Phi", gamma = 0.95, alpha = 1, niter = 100, C_eta = 1, ndrawings = 10, naveraging = 1 )
u1 |
vector of observations of the first coordinate, in [0,1]. |
u2 |
vector of observations of the second coordinate, in [0,1]. |
method |
a character giving the name of the estimation method, among:
|
par.start |
starting parameter of the gradient descent.
(only used for |
kernel |
the kernel used in the MMD distance
(only used for
Each of these names can receive the suffix |
gamma |
parameter γ to be used in the kernel.
(only used for |
alpha |
parameter α to be used in the kernel, if any.
(only used for |
niter |
the stochastic gradient algorithm is composed of two phases:
a first "burn-in" phase and a second "averaging" phase.
If |
C_eta |
a multiplicative constant controlling for the size of the gradient descent step.
The step size is then computed as |
ndrawings |
number of replicas of the stochastic estimate of the gradient
drawn at each step. The gradient is computed using the average of these replicas.
(only used for |
naveraging |
number of full run of the stochastic gradient algorithm
that are averaged at the end to give the final estimated parameter.
(only used for |
the estimated parameter (alpha
) of the Marshall-Olkin copula.
Alquier, P., Chérief-Abdellatif, B.-E., Derumigny, A., and Fermanian, J.D. (2022). Estimation of copulas via Maximum Mean Discrepancy. Journal of the American Statistical Association, doi: 10.1080/01621459.2021.2024836.
BiCopSim.MO
for the estimation of
Marshall-Olkin copulas.
BiCopEstMMD
for the estimation of other parametric copula families by MMD.
U <- BiCopSim.MO(n = 1000, alpha = 0.2) estimatedPar <- BiCopEst.MO(u1 = U[,1], u2 = U[,2], method = "MMD", niter = 1, ndrawings = 1) estimatedPar <- BiCopEst.MO(u1 = U[,1], u2 = U[,2], method = "MMD")
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