Multi-value conditional GPD profile likelihood confidence intervals

For non-stationary models, the quantile reparametrization depends on covariate values. This function repeats the profile likelihood procedure for several covariate values. It enables obtaining a quantile (or endpoint) curve, with profile-likelihood confidence bands, as a function of the covariate values.

Usage

GPD_profile_CIs_multiple(
  Y,
  threshold = 0,
  threshold_lvl = 0,
  parameter = c("quantile", "endpoint"),
  alpha = 0.05,
  quantile_lvl = 1 - (1/100),
  orthogonal = FALSE,
  X = NULL,
  X_rlvl = NULL,
  scale_cols = NULL,
  shape_cols = NULL,
  init_step_pos = 100,
  init_step_neg = 10,
  tol = 0.01,
  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"),
  parallel_strat = c("none", "multisession", "sequential", "multicore"),
  n_workers = NULL,
  ...
)

Arguments

Y: Data observations.
threshold: GPD threshold value.
threshold_lvl: Probability level of the threshold threshold.
parameter: Parameter for which to compute the profile likelihood confidence intervals.
alpha: Confidence alpha for the profile likelihood confidence intervals.
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 matrix at which to reparametrize for the 'quantile' or 'endpoint' parametrizations (for conditional/non-stationary fits). Columns should be variables, and each row should give one covariate realization at which to reparametrize and obtain a CI.
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).
init_step_pos: Initial numerical size of each evaluation step to the right, in the profile parameter's scale.
init_step_neg: Initial numerical size of each evaluation step to the left, in the profile parameter's scale.
tol: Numerical tolerance for convergence, 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.
parallel_strat: Parallel strategy. One of "sequential" (default), "multisession", "multicore", or "mixed".
n_workers: A positive numeric scalar or a function specifying the maximum number of parallel futures that can be active at the same time before blocking. If a function, it is called without arguments when the future is created and its value is used to configure the workers. The function should return a numeric scalar. Defaults to future::availableCores()-1 if NULL (default), with "multicore" constraint in the relevant case. Ignored if strategy=="sequential".
...: Other arguments passed to the control argument of stats::optim().

Value

The GPD profile log-likelihood (1-alpha) confidence intervals for the desired parameter, for each desired covariate values, as a tibble::tibble(), with columns:

obs: Index of the observation (i.e. row) of X_rlvl for which the parameter estimate and CI was computed.
<parameter name>: Conditional estimate of the parameter.
ci_down: Lower endpoint of the conditional (1-alpha) profile-likelihood confidence interval for parameter.
ci_up: Upper endpoint of the conditional (1-alpha) profile-likelihood confidence interval for parameter.
parameter: Name of the parameter for which the estimates and CIs were computed.
alpha: Confidence alpha for the profile likelihood confidence intervals.
quantile_lvl: Quantile probability level for 'quantile' parameter (only if parameter==quantile).