R: Parameter fitting for Huesler-Reiss graphical models

fmpareto_graph_HR {graphicalExtremes}

R Documentation

Parameter fitting for Huesler-Reiss graphical models

Description

Fits the parameter matrix (variogram) of a multivariate Huesler-Reiss Pareto distribution with a given graphical structure, using maximum-likelihood estimation or the empirical variogram.

Usage

fmpareto_graph_HR(
  data,
  graph,
  p = NULL,
  method = c("vario", "ML"),
  handleCliques = c("average", "full", "sequential"),
  ...
)

Arguments

`data`	Numeric `n \times d` matrix, where `n` is the number of observations and `d` is the number of dimensions.
`graph`	Undirected, connected [`igraph::graph`] object with `d` vertices, representing the graphical structure of the fitted Huesler-Reiss model.
`p`	Numeric between 0 and 1 or `NULL`. If `NULL` (default), it is assumed that the `data` is already on a multivariate Pareto scale. Else, `p` is used as the probability in the function `data2mpareto()` to standardize the `data`.
`method`	One of `c('vario', 'ML')`, with `'vario'` as default, indicating the method to be used for parameter estimation. See details.
`handleCliques`	How to handle cliques and separators in the graph. See details.
`...`	Arguments passed to `fmpareto_HR_MLE()`. Currently `cens`, `maxit`, `optMethod`, and `useTheta` are supported.

Details

If handleCliques='average', the marginal parameter matrix is estimated for each maximal clique of the graph and then combined into a partial parameter matrix by taking the average of entries from overlapping cliques. Lastly, the full parameter matrix is computed using complete_Gamma().

If handleCliques='full', first the full parameter matrix is estimated using the specified method and then the non-edge entries are adjusted such that the final parameter matrix has the graphical structure indicated by graph.

If handleCliques='sequential', graph must be decomposable, and method='ML' must be specified. The parameter matrix is first estimated on the (recursive) separators and then on the rest of the cliques, keeping previously estimated entries fixed.

If method='ML', the computational cost is mostly influenced by the total size of the graph (if handleCliques='full') or the size of the cliques, and can already take a significant amount of time for modest dimensions (e.g. d=3).

Value