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Mean and covariance of incomplete multivariate normal data

`ecmnmle(`

with no output arguments,
this mode displays the convergence of the ECM algorithm in a plot by estimating
objective function values for each iteration of the ECM algorithm until termination. `Data`

)

`[`

estimates the mean and covariance of a data set (`Mean`

,`Covariance`

] = ecmnmle(`Data`

)`Data`

). If the
data set has missing values, this routine implements the ECM algorithm of Meng and
Rubin [2] with enhancements by Sexton and Swensen [3]. ECM stands for a conditional
maximization form of the EM algorithm of Dempster, Laird, and Rubin [4].

`[`

adds an optional arguments for `Mean`

,`Covariance`

] = ecmnmle(___,`InitMethod`

,`MaxIterations`

,`Tolerance`

,`Mean0`

,`Covar0`

)`InitMethod`

,
`MaxIterations`

,
`Tolerance`

,`Mean0`

, and
`Covar0`

.

[1] Little, Roderick J. A. and
Donald B. Rubin. *Statistical Analysis with Missing Data.* 2nd
Edition. John Wiley & Sons, Inc., 2002.

[2] Meng, Xiao-Li and Donald B.
Rubin. “Maximum Likelihood Estimation via the ECM Algorithm.”
*Biometrika.* Vol. 80, No. 2, 1993, pp. 267–278.

[3] Sexton, Joe and Anders Rygh
Swensen. “ECM Algorithms that Converge at the Rate of EM.”
*Biometrika.* Vol. 87, No. 3, 2000, pp. 651–662.

[4] Dempster, A. P., N. M. Laird,
and Donald B. Rubin. “Maximum Likelihood from Incomplete Data via the EM
Algorithm.” *Journal of the Royal Statistical Society.*
Series B, Vol. 39, No. 1, 1977, pp. 1–37.