GPD profile log-likelihood

Usage

GPD_profile_loglik(
  val,
  Y,
  threshold = 0,
  threshold_lvl = 0,
  parameter = c("shape", "scale", "quantile", "endpoint"),
  subparam_id = 0,
  quantile_lvl = 1 - (1/100),
  orthogonal = FALSE,
  X = NULL,
  x_rlvl = NULL,
  scale_cols = NULL,
  shape_cols = NULL,
  obs_weights = NULL,
  ill_defined_value = -10^6,
  init = NULL,
  hessian = TRUE,
  maxit = 1e+06,
  method = c("Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", "Brent"),
  ...
)

Arguments

val: Parameter value at which to evaluate the GPD profile log-likelihood.
Y: Data observations.
threshold: GPD threshold value.
threshold_lvl: Probability level of the threshold threshold.
parameter: Parameter for which to compute the profile log-likelihood.
subparam_id: Index of the parameter coefficient for which to compute the profile log-likelihood (for conditional/non-stationary fits).
quantile_lvl: Quantile probability level for the 'quantile' parameter.
orthogonal: DEPRECATED.
X: Covariate matrix (for conditional/non-stationary fits). Columns should be variables, and rows should be observations matching Y.
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).
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).
init: Optional initial values for the remaining parameter's optimisation process, in the correct internal format.
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.
...: Other arguments passed to the control argument of stats::optim().

Value

The GPD profile log-likelihood of parameter evaluated at val, given the data, as a GPD_profML object containing:

param_val: (Named) parameter value at which the GPD profile log-likelihood was evaluated.
param_name: Name of the evaluated profile likelihood parameter.
mle_other: Maximum-likelihood estimate of the other GPD parameters.
loglik: Profile GPD log-likelihood value of parameter evaluated at val, 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.
parameter: Name of the evaluated profile likelihood parameter given as argument (redundent).
parametrization: Likelihood parametrization.
subparam_id: Index of the parameter coefficient for which the profile log-likelihood was computed.
id_param: Index of the likelihood profile parameter, in the internal parameter vector format.