R/MARSSFisherI.r

In eeholmes/MARSS: Multivariate Autoregressive State-Space Modeling

#######################################################################################################
#   MARSSFisherI function
#   Compute the observed Fisher Information Matrix at the values in the MLEobj

#   Compute the Fisher Information Matrix via Harvey (1989) and Cavanaugh & Shumway (1996) methods
#   Louis (1982) is nicely related to the derivatives used by the EM algorithm, but the
#   temporally correlation must be dealt with, e.g. Duan & Fulop (2011) A stable estimator of the information matrix
#   under EM for dependent data. Statistics and Computing 21: 83-91
#   Oakes (1999) has an approach that only involves derivatives of E(LL(theta)|data,theta') but one of the derivatives
#   will be the derivative of the E(X|data,theta') with respect to theta'.  It's not clear how to do that derivative.
#   Ho, Shumway and Ombao (2006) The state-space approach to modeling dynamic processes in Models for Intensive Longitudinal Data
#   page 157 suggest that this derivative is hard to compute.
#######################################################################################################
MARSSFisherI <- function(MLEobj, method = c("Harvey1989", "fdHess", "optim")) {
  # optim is here for debugging.  fdHess is the numerical method used for users
  method <- match.arg(method)
  if (method == "fdHess" || method == "optim") {
    obsFI <- MARSShessian.numerical(MLEobj, fun = method)
  }
  if (method == "Harvey1989") {
    obsFI <- MARSSharveyobsFI(MLEobj)
  }
  return(obsFI)
}