Estimating the number of classes

Details Estimating the number of classes Estimating the number of classes

2007-08-16

arxiv.org/abs/0708.2153v1

Annals of Statistics 2007, Vol. 35, No. 2, 917-930

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000001280 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000001280

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.

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