Open Access
April 2007 Estimating the number of classes
Chang Xuan Mao, Bruce G. Lindsay
Ann. Statist. 35(2): 917-930 (April 2007). DOI: 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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Chang Xuan Mao. Bruce G. Lindsay. "Estimating the number of classes." Ann. Statist. 35 (2) 917 - 930, April 2007.


Published: April 2007
First available in Project Euclid: 5 July 2007

zbMATH: 1117.62045
MathSciNet: MR2336874
Digital Object Identifier: 10.1214/009053606000001280

Primary: 62G15 , 62G15
Secondary: 62G05

Keywords: Hankel matrix , Moment problem , One-sided inference

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 2 • April 2007
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