beed.confband {ExtremalDep}  R Documentation 
Computes nonparametric bootstrap (1\alpha)\%
confidence bands for the Pickands dependence function.
beed.confband(data, x, d = 3, est = c("ht","md","cfg","pick"),
margin=c("emp", "est", "exp", "frechet", "gumbel"), k = 13,
nboot = 500, y = NULL, conf = 0.95, plot = FALSE, print = FALSE)
data 

x 

d 
postive integer (greater than or equal to two) indicating the number of variables ( 
est 
string denoting the estimation method (see Details). 
margin 
string denoting the type marginal distributions (see Details). 
k 
postive integer denoting the order of the Bernstein polynomial ( 
nboot 
postive integer indicating the number of bootstrap replicates. 
y 
numeric vector (of size 
conf 
real value in 
plot 
logical; 
print 
logical; 
Two methods for computing bootstrap (1\alpha)\%
pointwise and simultaneous confidence bands for the Pickands dependence function are used.
The first method derives the confidence bands computing the pointwise \alpha/2
and 1\alpha/2
quantiles of the bootstrap sample distribution of the Pickands dependence Bernstein based estimator.
The second method derives the confidence bands, first computing the pointwise \alpha/2
and 1\alpha/2
quantiles of the bootstrap sample distribution of polynomial coefficient estimators, and then the Pickands dependence is computed using the Bernstein polynomial representation. See Marcon et al. (2017) for details.
Most of the settings are the same as in the function beed
.
A 
numeric vector of the Pickands dependence function estimated. 
bootA 
matrix with 
A.up.beta/A.low.beta 
vectors of upper and lower bands of the Pickands dependence function obtained using the bootstrap sampling distribution of the polynomial coefficients estimator. 
A.up.pointwise/A.low.pointwise 
vectors of upper and lower bands of the Pickands dependence function obtained using the bootstrap sampling distribution of the Pickands dependence function estimator. 
up.beta/low.beta 
vectors of upper and lower bounds of the bootstrap sampling distribution of the polynomial coefficients estimator. 
This routine relies on the bootstrap routine (see beed.boot
).
Simone Padoan, simone.padoan@unibocconi.it, https://mypage.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com/; Giulia Marcon, giuliamarcongm@gmail.com
Marcon, G., Padoan, S.A., Naveau, P., Muliere, P. and Segers, J. (2017) Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials. Journal of Statistical Planning and Inference, 183, 117.
if (interactive()){
x < ExtremalDep:::simplex(2)
data < rbvevd(50, dep = 0.4, model = "log", mar1 = c(1,1,1))
# Note you should consider 500 bootstrap replications.
# In order to obtain fastest results we used 50!
cb < beed.confband(data, x, 2, "md", "emp", 20, 50, plot=TRUE)
}