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

fmpareto_HR_MLE {graphicalExtremes}

R Documentation

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 `n \times d` 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: