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Numerical saddlepoint equation solver

Source: R/B-optimization-functions.R
saddlepoint.solve.Rd

Solves the saddlepoint equation \(K1(t; \theta) = y\) for a given CGF object. It uses numeric optimization (via nloptr) to find the vector \(t\) that satisfies \(K1(t; \theta) = y\).

If the CGF object offers an analytical solution (see cgf_object$analytic_tvec_hat if available), you may prefer that approach instead.

Usage

saddlepoint.solve(
  theta,
  y,
  cgf,
  starting.tvec = rep(0, times = length(y)),
  lb = rep(-Inf, times = length(y)),
  ub = rep(Inf, times = length(y)),
  sadd.eqn.opts = list(ftol_abs = 0, maxeval = 1000, xtol_rel = 1e-12, print_level = 0),
  warn_residual = TRUE,
  tol = 1e-04
)

Arguments

theta

Numeric vector of model parameters for which the CGF is defined.

y

Numeric vector of observations.

cgf

A CGF object (class "CGF").

starting.tvec

Numeric start values for \(t\), defaults to 0 for each element.

lb, ub

Numeric vectors for lower and upper bounds of \(t\), each having the same length as starting.tvec. Defaults are -Inf and Inf.

sadd.eqn.opts

List of options for the nloptr optimizer. Defaults to list(ftol_abs = 0, maxeval = 1e3, xtol_rel = 1.0e-12, print_level = 0), with algorithm fixed at "NLOPT_LD_SLSQP".

warn_residual

Logical. If TRUE, compute the residual \(\|\mathit{K1}(t^*;\theta)-y\|_\infty\) and warn if it exceeds tol.

tol

Numeric tolerance for residual checks (default 1e-4).

Value

A numeric vector \(t\) solving \(K1(t, \theta) = y\).

Details

Minimizes the function \(K(t; \theta) - \sum(t_i y_i)\) to enforce \(K1(t, \theta) = y\).

References

Examples

if (FALSE) { # \dontrun{
# TO DO: Add examples
} # }