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\noindent Statistica Sinica {\bf 13}(2003), 655-671

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\centerline{\large\bf USING AUXILIARY INFORMATION FOR IMPROVING}
\vspace{2pt}
\centerline{\large\bf ESTIMATION IN THE NUMBER OF SPECIES PROBLEM}
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\author{S. Lynne Stokes}
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\centerline{\it Southern Methodist University}
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\begin{quotation}
\noindent {\it Abstract:}
Researchers from a variety of disciplines have studied the problem of
estimating the number of distinct classes in a population, known in statistics
as the number of species problem. The topic of this paper is the special case
of the problem in which the population is finite, its size (or the sampling
rate) is known, and auxiliary information correlated to class size is available
from sampled classes. We use this information to improve estimation by linking
class size to this information via a loglinear model. The parameters of the
model are estimated from the sample using conditional maximum likelihood, where
the conditioning event is that the class is observed in the sample. The model
is then used to estimate the probability of observation for every sampled
class, which is in turn used in a Horvitz-Thompson-like estimator of number of
classes. The paper shows that the improvement in estimation over other
available estimators can be dramatic, especially if the class sizes vary
widely. The performance of the estimator degrades when the model is
misspecified, but still competes well with alternative estimators.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
capture-recapture, Horvitz-Thompson estimator, loglinear model, number of
classes.\par
\end{quotation}
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