Standard errors for mean and covariance of incomplete data
[StdMean, StdCovariance] = ecmnstd(Data, Mean, Covariance, Method)






 (Optional) String indicating method of estimation for standard error calculations. The methods are:

[StdMean, StdCovariance] = ecmnstd(Data, Mean, Covariance,
Method)
computes standard errors for mean and covariance
of incomplete data.
StdMean
is a NUMSERIES
by1
column
vector of standard errors of estimates for each element
of the mean vector Mean
.
StdCovariance
is a NUMSERIES
byNUMSERIES
matrix
of standard errors of estimates for each element of the covariance
matrix Covariance
.
Use this routine after estimating the mean and covariance of Data
with ecmnmle
.
If the mean and distinct covariance elements are treated as the parameter θ in
a completedata maximumlikelihood estimation, then as the number
of samples increases, θ attains asymptotic
normality such that
$$\theta E\left[\theta \right]\sim N\left(0,{I}^{1}\left(\theta \right)\right),$$
where E[θ] is the mean and I(θ) is the Fisher information matrix.
With missing data, the Hessian H(θ) is a good approximation for the Fisher information (which can only be approximated when data is missing).
It is usually advisable to use the default Method
since
the resultant standard errors incorporate the increased uncertainty
due to missing data. In particular, standard errors calculated with
the Hessian are generally larger than standard errors calculated with
the Fisher information matrix.
Note
This routine is very slow for 