Compute nonparametric bootstrap *(1-α)\%* confidence bands for the Pickands dependence function.

1 2 3 |

`data` |
A |

`x` |
A |

`d` |
A postive integer (greater than or equal to two) indicating the number of variables.
The trivariate case |

`est` |
A string denoting the estimation method (see |

`margin` |
A string denoting the type marginal distributions (see |

`k` |
A postive integer denoting the order of the Bernstein polynomial. |

`nboot` |
A postive integer indicating the number of bootstrap replicates. |

`y` |
A numeric vector (of size |

`conf` |
A real value in |

`matrix` |
Logical; |

`plot` |
Logical; |

`print` |
Logical; |

Two methods for computing bootstrap *(1-α)\%* point-wise and simultaneous confident bands for the Pickands dependence function are used.

The first method derives the confidence bands computing the point-wise *α/2*
and *1-α/2* quantiles of the bootstrap sample distribution of the Pickands dependence Bernstein based estimator.

The second method derives the confidence bands, first computing the point-wise *α/2*
and *1-α/2* quantiles of the bootstrap sample distribution of polynomial coefficients estimators, and then
the Pickands dependence is computed using the Bernstein polynomial representation. See Marcon et al. (2014) for details.

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

.

`A` |
Estimate of the Pickands dependence function. |

`bootA` |
A 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, faculty.bocconi.it/simonepadoan; Giulia Marcon

Marcon, G., Padoan, S.A., Naveau, P., Muliere, P. and Segers, J. (2016)
Multivariate Nonparametric Estimation of the Pickands Dependence
Function using Bernstein Polynomials.
*Journal of Statistical Planning and Inference*, **To appear**.

`beed`

, `beed.boot`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
## Not run:
w <- seq(0, 1, length = 100)
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, cbind(w, 1-w), 2, 'md', 'emp', 20, 50)
plot(w, w, type='n', xlab="w", ylab="A(w)", ylim=c(.5,1))
polygon(c(0, 0.5, 1), c(1, 0.5, 1), lty=1, lwd=1, border='grey')
lines(w, cb$A, lty=1)
lines(w, cb$A.up.beta, lty=2)
lines(w, cb$A.low.beta, lty=2)
## End(Not run)
``` |

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