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Estimating the number of classes. (English) Zbl 1117.62045
Summary: Estimating the unknown number of classes in a population has numerous important applications. In a Poisson mixture model, the problem is reduced to estimating the odds that a class is undetected in a sample. The discontinuity of the odds prevents the existence of locally unbiased and informative estimators and restricts confidence intervals to be one-sided. Confidence intervals for the number of classes are also necessarily one-sided. A sequence of lower bounds to the odds is developed and used to define pseudo maximum likelihood estimators for the number of classes.

MSC:
62G15 Nonparametric tolerance and confidence regions
62G05 Nonparametric estimation
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