Efficient ML Estimation of the Multivariate Normal Distribution from Incomplete Data
| Autor: | Chuanhai Liu |
|---|---|
| Rok vydání: | 1999 |
| Předmět: |
Statistics and Probability
Numerical Analysis Fisher information MEM monotone pattern Multivariate normal distribution Missing data ECME MECME symbols.namesake Monotone polygon Efficient estimator Complete information Expectation–maximization algorithm Linear regression Statistics linear regression symbols Statistics::Methodology Applied mathematics Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Journal of Multivariate Analysis. 69:206-217 |
| ISSN: | 0047-259X |
| DOI: | 10.1006/jmva.1998.1793 |
| Popis: | It is well known that the maximum likelihood estimates (MLEs) of a multivariate normal distribution from incomplete data with a monotone pattern have closed-form expressions and that the MLEs from incomplete data with a general missing-data pattern can be obtained using the Expectation-Maximization (EM) algorithm. This article gives closed-form expressions, analogous to the extension of the Bartlett decomposition, for both the MLEs of the parameters and the associated Fisher information matrix from incomplete data with a monotone missing-data pattern. For MLEs of the parameters from incomplete data with a general missing-data pattern, we implement EM and Expectation-Constrained-Maximization-Either (ECME), by augmenting the observed data into a complete monotone sample. We also provide a numerical example, which shows that the monotone EM (MEM) and monotone ECME (MECME) algorithms converge much faster than the EM algorithm. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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