maxstabtest | R Documentation |

The diagnostic, proposed by Gabda, Towe, Wadsworth and Tawn,
relies on the fact that, for max-stable vectors on the unit Gumbel scale,
the distribution of the maxima is Gumbel distribution with a location parameter equal to the exponent measure.
One can thus consider tuples of size `m`

and estimate the location parameter via maximum likelihood
and transforming observations to the standard Gumbel scale. Replicates are then pooled and empirical quantiles are defined.
The number of combinations of `m`

vectors can be prohibitively large, hence only `nmax`

randomly selected
tuples are selected from all possible combinations. The confidence intervals are obtained by a
nonparametric bootstrap, by resampling observations with replacement observations for the selected tuples and re-estimating the
location parameter. The procedure can be computationally intensive as a result.

maxstabtest( dat, m = prod(dim(dat)[-1]), nmax = 500L, B = 1000L, ties.method = "random", plot = TRUE )

`dat` |
matrix or array of max-stable observations, typically block maxima. The first dimension should consist of replicates |

`m` |
integer indicating how many tuples should be aggregated. |

`nmax` |
maximum number of pairs. Default to 500L. |

`B` |
number of nonparametric bootstrap replications. Default to 1000L. |

`ties.method` |
string indicating the method for |

`plot` |
logical indicating whether a graph should be produced (default to |

a Tukey probability-probability plot with 95

Gabda, D.; Towe, R. Wadsworth, J. and J. Tawn, Discussion of “Statistical Modeling of Spatial Extremes” by A. C. Davison, S. A. Padoan and M. Ribatet. *Statist. Sci.* **27** (2012), no. 2, 189–192.

## Not run: dat <- mev::rmev(n = 250, d = 100, param = 0.5, model = "log") maxstabtest(dat, m = 100) maxstabtest(dat, m = 2, nmax = 100) dat <- mev::mvrnorm(n = 250, Sigma = diag(0.5, 10) + matrix(0.5, 10, 10), mu = rep(0, 10)) maxstabtest(dat, m = 2, nmax = 100) maxstabtest(dat, m = ncol(dat)) ## End(Not run)

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