Compute standard error and inverse Hessian

This function calculates the standard error and the inverse of the Hessian matrix for a model incorporating both the saddlepoint likelihood and an optional non-saddlepoint negative log-likelihood component.

Usage

compute.std.error(
  observed.data,
  estimated.tvec,
  estimated.theta,
  cgf,
  zeroth.order = FALSE,
  non.saddlepoint.negll.function = NULL
)

Arguments

observed.data

A numeric vector of observations used in the saddlepoint likelihood calculations.

estimated.tvec

A numeric vector of MLE values for the saddlepoint values tvec.

estimated.theta

A numeric vector of MLE values for the model parameters.

cgf

A CGF object used in the saddlepoint likelihood computation.

zeroth.order

A logical value indicating whether the zeroth-order saddlepoint likelihood is used. Default is FALSE.

non.saddlepoint.negll.function

An optional function specifying a non-saddlepoint negative log-likelihood. If your model used for estimation incorporates a likelihood component that is not based on the saddlepoint approximation, this function must be provided. See details for more information.

Value

A list containing:

• std.error: Standard error computed from the diagonal of the inverse Hessian.

• inverse.hessian: Inverse of the Hessian matrix.

Details

The non.saddlepoint.negll.function, if provided, should have the form: $$function(theta) \{ return(list(objective = ..., hessian = ...)) \}$$ It adds flexibility by allowing incorporation of likelihood components not based on the saddlepoint likelihood. It is important when the analysis combines the saddlepoint likelihood with an external likelihood. If not provided, the function defaults to using solely the saddlepoint likelihood.

Examples

# TODO: Add examples