emst: Fitting extremal minimum spanning tree

In sebastian-engelke/graphicalExtremes: Statistical Methodology for Graphical Extreme Value Models

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 \insertCiteeng2019;textualgraphicalExtremes for details.

• empirical extremal variogram, if method = "vario". See \insertCiteeng2020;textualgraphicalExtremes for details.

• empirical extremal correlation, if method = "chi". See \insertCiteeng2020;textualgraphicalExtremes for details.

Usage

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

Arguments

data	Numeric \nxd 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 \dxd estimated variogram matrix \eGamma corresponding to the fitted minimum spanning tree.

References

\insertAllCited

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)

sebastian-engelke/graphicalExtremes documentation built on Jan. 10, 2025, 10:02 a.m.