Estimating the number of classes

TL;DR

This paper addresses the challenge of estimating the unknown number of classes in a population using Poisson mixture models, highlighting the difficulties due to discontinuities and proposing lower bounds and pseudo maximum likelihood estimators.

Contribution

It introduces a novel approach using lower bounds to estimate the number of classes, overcoming issues with discontinuous odds in Poisson mixture models.

Findings

Developed a sequence of lower bounds for the odds

Defined pseudo maximum likelihood estimators based on these bounds

Provided one-sided confidence intervals for the number of classes

Abstract

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.