fmpareto_HR_MLE: Parameter fitting for multivariate Huesler-Reiss Pareto...

In graphicalExtremes: Statistical Methodology for Graphical Extreme Value Models

Parameter fitting for multivariate Huesler-Reiss Pareto distribution

Description

Fits the parameters of a multivariate Huesler-Reiss Pareto distribution using (censored) maximum likelihood estimation.

Usage

fmpareto_HR_MLE(
  data,
  p = NULL,
  cens = FALSE,
  init = NULL,
  fixParams = integer(0),
  useTheta = TRUE,
  maxit = 100,
  graph = NULL,
  optMethod = "BFGS",
  nAttemptsFixInit = 3
)

Arguments

data	Numeric \nxd matrix, where n is the number of observations and d is the number of dimensions.
p	Numeric scalar 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 data2mpareto() to standardize the data.
cens	Logical scalar. If true, then censored likelihood contributions are used for components below the threshold. This is computationally expensive and by default cens = FALSE.
init	Numeric vector or numeric matrix. Initial parameter values in the optimization. If NULL, the empirical variogram is used instead. Otherwise should be a numeric vector with one entry per edge in graph, or a complete variogram/precision matrix.
fixParams	Numeric or logical vector. Indices of the parameter vectors that are kept fixed (identical to init) during the optimization. Default is integer(0).
useTheta	Logical. Whether to perform the MLE optimization in terms of Theta or Gamma.
maxit	Positive integer. The maximum number of iterations in the optimization.
graph	Graph object from igraph package or NULL (implying the complete graph).
optMethod	String. A valid optimization method used by the function stats::optim. By default, method = "BFGS".
nAttemptsFixInit	Numeric. If useTheta=TRUE and the initial parameter init is not valid, attempt to fix it first by making sure all off-diagonal entries are negative and then adding some random noise at most this many times.

Details

Only the parameters corresponding to edges in graph are optimized, the remaining entries are implied by the graphical structure. If graph is NULL, the complete graph is used. The optimization is done either in terms of the variogram (Gamma) or precision matrix (Theta), depending on the value of useTheta. If graph is non-decomposable, useTheta=TRUE is significantly faster, otherwise they are similar in performance.

Value

List consisting of:

convergence	Logical. Indicates whether the optimization converged or not.
Gamma	Numeric ⁠d x d⁠ matrix. Fitted variogram matrix.
Theta	Numeric ⁠d x d⁠ matrix. Fitted precision matrix.
par	Numeric vector. Optimal parameters, including fixed parameters.
par_opt	Numeric. Optimal parameters, excluding fixed parameters.
nllik	Numeric. Optimal value of the negative log-likelihood function.
hessian	Numeric matrix. Estimated Hessian matrix of the estimated parameters.

See Also

Other parameter estimation methods: data2mpareto(), emp_chi(), emp_chi_multdim(), emp_vario(), emtp2(), fmpareto_graph_HR(), loglik_HR()

graphicalExtremes documentation built on April 3, 2025, 6:22 p.m.