On the use of the selection matrix in the maximum likelihood estimation of normal distribution models with missing data |
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Authors: | Keiji Takai |
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Institution: | 1. Faculty of Business and Commerce, Kansai University, Japantakai@kansai-u.ac.jp |
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Abstract: | In this article, by using the constant and random selection matrices, several properties of the maximum likelihood (ML) estimates and the ML estimator of a normal distribution with missing data are derived. The constant selection matrix allows us to obtain an explicit form of the ML estimates and the exact relationship between the EM algorithm and the score function. The random selection matrix allows us to clarify how the missing-data mechanism works in the proof of the consistency of the ML estimator, to derive the asymptotic properties of the sequence by the EM algorithm, and to derive the information matrix. |
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Keywords: | EM algorithm Information matrix Maximum likelihood estimator Missing data Normal distribution Selection matrix |
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