Description Usage Arguments Value References See Also Examples
View source: R/MarshallOlkin.R
Estimation of MarshallOlkin copulas
1 2 3 4 5 6 7 8 9 10 11 12 13  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 ".Phi", such as "gaussian.Phi" to indicates that the kernel k(x,y) is replaced by k(Φ^{1}(x) , Φ^{1}(y)) where Φ^{1} denotes the quantile function of the standard Normal distribution. 
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 "burnin" 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 MarshallOlkin copula.
Alquier, P., ChériefAbdellatif, B.E., Derumigny, A., and Fermanian, J.D. (2020). Estimation of copulas via Maximum Mean Discrepancy. ArXiv preprint arxiv:2010.00408
BiCopSim.MO
for the estimation of
MarshallOlkin copulas.
BiCopEstMMD
for the estimation of other parametric copula families by MMD.
1 2 3 4  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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