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.
Publié le : 2007-04-14
Classification:
Hankel matrix,
moment problem,
one-sided inference,
62G15,
62G15,
62G05
@article{1183667299,
author = {Mao, Chang Xuan and Lindsay, Bruce G.},
title = {Estimating the number of classes},
journal = {Ann. Statist.},
volume = {35},
number = {1},
year = {2007},
pages = { 917-930},
language = {en},
url = {http://dml.mathdoc.fr/item/1183667299}
}
Mao, Chang Xuan; Lindsay, Bruce G. Estimating the number of classes. Ann. Statist., Tome 35 (2007) no. 1, pp. 917-930. http://gdmltest.u-ga.fr/item/1183667299/