Strong consistency of MLE for finite uniform mixtures when the scale parameters are exponentially small |
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| Authors: | Kentaro Tanaka Akimichi Takemura |
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| Institution: | (1) The Department of Industrial Engineering and Management, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8552 Tokyo, Japan;(2) Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Bunkyo-ku, 113-0033 Tokyo, Japan |
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| Abstract: | We consider maximum likelihood estimation of finite mixture of uniform distributions. We prove that maximum likelihood estimator
is strongly consistent, if the scale parameters of the component uniform distributions are restricted from below by exp(−n
d
), 0<d<1, wheren is the sample size. |
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| Keywords: | Mixture distribution maximum likelihood estimator consistency |
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