Asymptotic Inference with Incomplete Data |
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Authors: | Keiji Takai Yutaka Kano |
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Institution: | 1. Data Mining Laboratory , Kansai University , Osaka , Japan takaikeiji+cs@gmail.com;3. Graduate School of Engineering Science , Osaka University , Osaka , Japan |
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Abstract: | This article discusses asymptotic theory for the maximum likelihood estimator based on incomplete data. Although much literature has implicitly assumed the basic properties of the estimator, such as consistency and asymptotic normality, it is hard to find their precise and comprehensive proofs. In this article, we first show that under MAR an estimator based on the likelihood function ignoring the missing-data mechanism is strongly consistent. The estimator is then shown to be asymptotically normal. When the data are NMAR and when the data are MAR without parameter distinctness, the consistency and the asymptotic normality are shown. Several examples are provided. |
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Keywords: | Asymptotic inference Incomplete data Missing at random Maximum likelihood estimator Not missing at random |
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