# beed.boot: 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.

## Value

Anumeric vector of the estimated Pickands dependence function.

bootAmatrix with `nboot`

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

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

## 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"`

).

## 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.

## Examples

# NOT RUN {
x <- ExtremalDep:::simplex(2)
data <- rbvevd(50, dep = 0.4, model = "log", mar1 = c(1,1,1))
boot <- beed.boot(data, x, 2, "md", "emp", 20, 500)
# }