Maximum-likelihood GPD estimate

Usage

GPD_maxlik(
  Y,
  threshold = 0,
  threshold_lvl = 0,
  parametrization = c("classical", "orthogonal", "quantile", "endpoint"),
  quantile_lvl = 1 - (1/100),
  orthogonal = FALSE,
  X = NULL,
  x_rlvl = NULL,
  scale_cols = NULL,
  shape_cols = NULL,
  out_param = parametrization,
  obs_weights = NULL,
  ill_defined_value = -10^6,
  hessian = TRUE,
  maxit = 1e+06,
  method = c("Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", "Brent"),
  verbose = 1,
  ...
)

Arguments

Y: Data observations.
threshold: GPD threshold value.
threshold_lvl: Probability level of the threshold threshold.
parametrization: Likelihood parametrization. Alternatives to classical substitute for the scale parameter.
quantile_lvl: Quantile probability level for the 'quantile' parametrization.
orthogonal: DEPRECATED.
X: Covariate matrix (for conditional/non-stationary fits).
x_rlvl: Covariate vector at which to reparametrize for the 'quantile' or 'endpoint' parametrizations (for conditional/non-stationary fits).
scale_cols: Column indices of X to use as covariate for the (conditional) scale parameter (for conditional/non-stationary fits).
shape_cols: Column indices of X to use as covariate for the (conditional) shape parameter (for conditional/non-stationary fits).
out_param: Additional output parametrization (same as parametrization, by default). If out_param != parametrization, the parameters are reparametrized from parametrization to out_param after estimation, in a separate output.
obs_weights: Optional observation weights for weighted likelihood.
ill_defined_value: Value to return if the arguments are out of support (e.g. negative scale, or non-positive arguments to logarithms).
hessian: Logical. Should a numerically differentiated Hessian matrix be returned? See stats::optim() for more details.
maxit: The maximum number of iterations. See stats::optim() for more details.
method: The optimisation method to be used. See stats::optim() for more details.
verbose: Verbose level, as integer.
...: Other arguments passed to the control argument of stats::optim().

Value

The fitted maximum-likelihood GPD as a GPD_ML object, containing:

mle: The estimated maximum likelihood GPD parameters, as a named vector (expressed in parametrization).
loglik: The log-likelihood of the estimated parameters, given the data
conv: Whether the optimisation procedure converged. See the convergence output of stats::optim() for more details.
hessian: The loglikelihood hessian evaluated at the estimated parameters, given the data.
parametrization: Likelihood parametrization.
out_mle: The estimated maximum likelihood GPD parameters, reparametrized in out_param.
out_parametrization: Additional output parametrization.