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Strong consistency of MLE for finite uniform mixtures when the scale parameters are exponentially small

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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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Authors and Affiliations

  1. The Department of Industrial Engineering and Management, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8552, Tokyo, Japan

    Kentaro Tanaka

  2. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Bunkyo-ku, 113-0033, Tokyo, Japan

    Akimichi Takemura

Authors
  1. Kentaro Tanaka
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  2. Akimichi Takemura
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Tanaka, K., Takemura, A. Strong consistency of MLE for finite uniform mixtures when the scale parameters are exponentially small. Ann Inst Stat Math 57, 1–19 (2005). https://doi.org/10.1007/BF02506875

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  • DOI: https://doi.org/10.1007/BF02506875

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