Standard errors for mean and covariance of incomplete data
[StdMean,StdCovariance] = ecmnstd(Data,Mean,Covariance,Method)
(Optional) Character vector 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
vector of standard errors of estimates for each element
of the mean vector
StdCovariance is a
of standard errors of estimates for each element of the covariance
Use this routine after estimating the mean and covariance of
If the mean and distinct covariance elements are treated as the parameter θ in
a complete-data maximum-likelihood estimation, then as the number
of samples increases, θ attains asymptotic
normality such that
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
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.
This routine is slow for
NUMSERIES > 10 or