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

Kentaro Tanaka; Akimichi Takemura

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arXiv · math/0409197

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

Kentaro Tanaka·Akimichi Takemura

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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, where n is the sample size.

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Kentaro Tanaka, Akimichi Takemura. 2004-09-13. Strong consistency of MLE for finite uniform mixtures when the scale parameters are exponentially small. https://arxiv.org/abs/math/0409197

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