beed.boot {ExtremalDep}

Bootstrap Resampling and Bernstein Estimation of Extremal Dependence

Description

Computes nboot estimates of the Pickands dependence function for multivariate data (using the Bernstein polynomials approximation method) on the basis of the bootstrap resampling of the data.

Usage

  beed.boot(data, x, d = 3, est = c("ht","md","cfg","pick"),
     margin=c("emp", "est", "exp", "frechet", "gumbel"), k = 13,
     nboot = 500, y = NULL, print = FALSE)

Arguments

data

n \times d matrix of component-wise maxima.

x

m \times d design matrix where the dependence function is evaluated, see Details.

d

postive integer (greater than or equal to two) indicating the number of variables (d=3 by default).

est

string denoting the preliminary estimation method (see Details).

margin

string denoting the type marginal distributions (see Details).

k

postive integer denoting the order of the Bernstein polynomial (k=13 by default).

nboot

postive integer indicating the number of bootstrap replicates (nboot=500 by default).

y

numeric vector (of size m) with an initial estimate of the Pickands function. If NULL, The initial estimation is performed by using the estimation method chosen in est.

print

logical; FALSE by default. If TRUE the number of the iteration is printed.

Details

Standard bootstrap is performed, in particular estimates of the Pickands dependence function are provided for each data resampling.

Most of the settings are the same as in the function beed.

An empirical transformation of the marginals is performed when margin="emp". A max-likelihood fitting of the GEV distributions is implemented when margin="est". Otherwise it refers to marginal parametric GEV theorethical distributions (margin = "exp", "frechet", "gumbel").

Value

A

numeric vector of the estimated Pickands dependence function.

bootA

matrix with nboot columns that reports the estimates of the Pickands function for each data resampling.

beta

matrix of estimated polynomial coefficients. Each column corresponds to a data resampling.

Author(s)

Simone Padoan, [e-mail], https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, [e-mail] https://www.borisberanger.com; Giulia Marcon, [e-mail]

References

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, 1-17.

See Also

beed, beed.confband.

Examples

x <- simplex(2)
data <- evd::rbvevd(50, dep = 0.4, model = "log", mar1 = c(1,1,1))

boot <- beed.boot(data, x, 2, "md", "emp", 20, 500)