Fisher information matrix
Fisher = ecmnfish(Data,Covariance,InvCovariance,MatrixFormat)
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| (Optional) Inverse of covariance matrix: |
| (Optional) Character vector that identifies parameters
included in the Fisher information matrix. If
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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 can be
smaller than the estimated standard errors derived from the expected
Hessian matrix. To see the difference, compare to standard errors
calculated with ecmnhess
.