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

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

2004-09-13

arxiv.org/abs/math/0409197v1

Annals of the Institute of Statistical Mathematics, 57 (2005), 1-19

Mathematics

Statistics Theory

20 pages, 1 figure

Scientific paper

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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