Compute the correction term for the saddlepoint approximation to the log-likelihood

This function calculates the correction term for the saddlepoint approximation to the log-likelihood. By default, it computes that of the first-order approximation, If spa_method="zeroth", it instead computes the correction term for the zeroth-order approximation.

Usage

compute.saddlepointLL.correction(
  parameter_vector,
  observed.data,
  cgf,
  tvec.hat = NULL,
  gradient = FALSE,
  hessian = FALSE,
  spa_method = "standard",
  tvec_source = c("auto", "user", "analytic", "newton", "solver_atomic"),
  solver_fun = saddlepoint.solve,
  newton_t_init = NULL,
  ...
)

Arguments

parameter_vector: Numeric vector of parameters.
observed.data: Numeric vector of observed data.
cgf: A CGF object.
tvec.hat: (Optional) Numeric vector. If supplied, tvec is taken directly as this vector (the saddlepoint \(\hat{t}\)). Otherwise we compute it (analytic if available, else numeric solve).
gradient: Logical. If TRUE, return gradient wrt parameter_vector.
hessian: Logical. If TRUE, return Hessian wrt parameter_vector.
spa_method: Character string. One of "standard" (first-order) or "zeroth".
tvec_source: One of "auto","user","analytic","newton","solver_atomic". See compute.spa.negll.
solver_fun: Numeric solver used when tvec_source="solver_atomic" or in non-AD path. Default saddlepoint.solve.
newton_t_init: Optional start for t in the Newton solver path.
...: Passed to solver_fun when used.

Value

A named list with elements:

val: Numeric scalar of the correction term.
gradient: The gradient at theta, if gradient=TRUE.
hessian: The Hessian at theta, if hessian=TRUE.

Usage

Arguments

Value

See also