GPD profile log-likelihood curve

Usage

GPD_profile_loglik_curve(
  Y,
  threshold = 0,
  threshold_lvl = 0,
  parameter = c("shape", "scale", "quantile", "endpoint"),
  subparam_id = 0,
  alpha = 0.05,
  quantile_lvl = 1 - (1/100),
  orthogonal = FALSE,
  X = NULL,
  x_rlvl = NULL,
  scale_cols = NULL,
  shape_cols = NULL,
  warmstart_table = NULL,
  stepsize = 0.1,
  steps_beyond_conf = 5,
  initial_MLE_para = c("classical", "same"),
  max_steps = 10000,
  obs_weights = NULL,
  ill_defined_value = -10^6,
  hessian = TRUE,
  maxit = 1e+06,
  method = c("Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", "Brent"),
  method_prof = c("default", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", "Brent"),
  ...
)

Arguments

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).
alpha: Confidence alpha for the profile log-likelihood confidence interval (i.e. for the confidence line on the profile plot).
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).
warmstart_table: Evaluation table from a previous run.
stepsize: Numerical size of each evaluation step, in the profile parameter's scale.
steps_beyond_conf: Number of additional steps to take (in each direction) after the profile log-likelihood values reach below the confidence line.
initial_MLE_para: Parametrization used for the initial maximum likelihood estimate (defaults to classical, for better stability).
max_steps: Maximum number of steps taken (in each direction). If the confidence line was not reached, the corresponding confidence interval endpoint will be infinite.
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 for the initial maximum likelihood optimisation. See stats::optim() for more details.
method_prof: The optimisation method to be used for the profile likelihood optimisation. See stats::optim() for more details.
...: Other arguments passed to the control argument of stats::optim().

Value

The GPD profile log-likelihood curve for the desired parameter, with confidence line and resulting (1-alpha) confidence interval, as a GPD_profileLogLik object containing:

mle: The estimated maximum likelihood GPD parameters, as a named vector (expressed in the profile parametrization).
ci: Length-two vector containing the lower and upper endpoints of the desired profile likelihood confidence interval.
profile_loglik: Named matrix containing the profile loglikelihood value (Column 2) for each considered profile parameter value (Column 1).
conf_line: Confidence line for the desired profile likelihood confidence interval. See e.g. Coles (2001) for more details.
eval_table: Tibble (tibble::tibble()) containing the history of profile log-likelihood evaluation values, and related metadata.
param_name: Name of the profiled parameter (infered, for debugging purposes).
parameter: Name of the profiled parameter (given).
parametrization: Parametrization used for the profile likelihood.
subparam_id: Index of the parameter coefficient for which the profile log-likelihood was computed.
id_param: Index of the profile parameter in the GPD parameter vector.

References

Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. doi:10.1007/978-1-4471-3675-0.