Fisher information matrix
Fisher = ecmnfish(Data, Covariance, InvCovariance, MatrixFormat)
NUMSAMPLES-by-NUMSERIES matrix of observed multivariate normal data
NUMSERIES-by-NUMSERIES matrix with covariance estimate of Data
(Optional) Inverse of covariance matrix: inv(Covariance)
(Optional) String that identifies parameters included in the Fisher information matrix. If MatrixFormat =  or ' ', the default method full is used. The parameter choices are
Fisher = ecmnfish(Data, Covariance, InvCovariance, MatrixFormat) computes a NUMPARAMS-by-NUMPARAMS Fisher information matrix based on current parameter estimates, where
NUMPARAMS = NUMSERIES*(NUMSERIES + 3)/2
if MatrixFormat = 'full' and
NUMPARAMS = NUMSERIES
if MatrixFormat = 'meanonly'.
The data matrix has NaNs for missing observations. The multivariate normal model has
NUMPARAMS = NUMSERIES + NUMSERIES*(NUMSERIES + 1)/2
distinct parameters. Therefore, the full Fisher information matrix is of size NUMPARAMS-by-NUMPARAMS. The first NUMSERIES parameters are estimates for the mean of the data in Mean, and the remaining NUMSERIES*(NUMSERIES + 1)/2 parameters are estimates for the lower-triangular portion of the covariance of the data in Covariance, in row-major order.
If MatrixFormat = 'meanonly', the number of parameters is reduced to NUMPARAMS = NUMSERIES, where the Fisher information matrix is computed for the mean parameters only. In this format, the routine executes fastest.
This routine expects the inverse of the covariance matrix as an input. If you do not pass in the inverse, the routine computes it. You can obtain an approximation for the lower-bound standard errors of estimation of the parameters from
Stderr = (1.0/sqrt(NumSamples)) .* sqrt(diag(inv(Fisher)));
Because of missing information, these standard errors may be smaller than the estimated standard errors derived from the expected Hessian matrix. To see the difference, compare to standard errors calculated with ecmnhess.