emst {graphicalExtremes}

Fitting extremal minimum spanning tree

Description

Fits an extremal minimum spanning tree, where the edge weights are:

• negative maximized log-likelihoods of the bivariate Huesler-Reiss distributions, if method = "ML". See Engelke and Hitz (2020) for details.

• empirical extremal variogram, if method = "vario". See Engelke and Volgushev (2022) for details.

• empirical extremal correlation, if method = "chi". See Engelke and Volgushev (2022) for details.

Usage

emst(data, p = NULL, method = c("vario", "ML", "chi"), cens = FALSE)

Arguments

data

Numeric n \times d matrix, where n is the number of observations and d is the dimension.

p

Numeric between 0 and 1 or NULL. If NULL (default), it is assumed that the data are already on multivariate Pareto scale. Else, p is used as the probability in the function data2mpareto() to standardize the data.

method

One of ⁠"vario", "ML", "chi"⁠. Default is method = "vario".

cens

Logical. This argument is considered only if method = "ML". If TRUE, then censored likelihood contributions are used for components below the threshold. By default, cens = FALSE.

Value

List consisting of:

graph

An igraph::graph object. The fitted minimum spanning tree.

Gamma

Numeric d \times d estimated variogram matrix \Gamma corresponding to the fitted minimum spanning tree.

References

Engelke S, Hitz AS (2020). “Graphical models for extremes (with discussion).” J. R. Stat. Soc. Ser. B Stat. Methodol., 82, 871–932.

Engelke S, Volgushev S (2022). “Structure learning for extremal tree models.” J. R. Stat. Soc. Ser. B Stat. Methodol.. doi:10.1111/rssb.12556, Forthcoming, https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/rssb.12556.

See Also

Other structure estimation methods: data2mpareto(), eglatent(), eglearn(), fit_graph_to_Theta()

Examples

## Fitting a 4-dimensional HR minimum spanning tree
my_graph <- igraph::graph_from_adjacency_matrix(
  rbind(
    c(0, 1, 0, 0),
    c(1, 0, 1, 1),
    c(0, 1, 0, 0),
    c(0, 1, 0, 0)
  ),
  mode = "undirected"
)
n <- 100
Gamma_vec <- c(.5, 1.4, .8)
complete_Gamma(Gamma = Gamma_vec, graph = my_graph) ## full Gamma matrix

set.seed(123)
my_data <- rmpareto_tree(n, "HR", tree = my_graph, par = Gamma_vec)
my_fit <- emst(my_data, p = NULL, method = "ML", cens = FALSE)