## Existence and consistency of maximum likelihood in upgraded mixture models.(English)Zbl 0752.62026

Summary: Suppose one observes a sample of size $$m$$ from the mixture density $$\int p(x\mid z)d\eta(z)$$ and a sample of size $$n$$ from the distribution $$\eta$$. The kernel $$p(x\mid z)$$ is known. We show existence of the maximum likelihood estimator for $$\eta$$, characterize its support, and prove consistency as $$m$$, $$n\to\infty$$.

### MSC:

 62F12 Asymptotic properties of parametric estimators 62G20 Asymptotic properties of nonparametric inference
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### References:

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