2007/04/01 by Chang Xuan Mao, Bruce G. Lindsay · 1 citation
Mathematics · Medicine · #Census and Population Estimation #Data-Driven Disease Surveillance #Survey Sampling and Estimation Techniques #math.ST #msc:62G05 #msc:62G15 #stat.TH
paper · pdf · doi:10.1214/009053606000001280
published as Annals of Statistics 2007, Vol. 35, No. 2, 917-930 · Published at http://dx.doi.org/10.1214/009053606000001280 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2007/04/01 · arxiv created 2007/08/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.