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\noindent Statistica Sinica {\bf 13}(2003), 243-254
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\centerline{\large\bf ESTIMATING POPULATION SIZE IN PROPORTIONAL}
\vspace{2pt}
\centerline{\large\bf TRAPPING-REMOVAL MODELS}
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\centerline{Liping Liu and Paul S. F. Yip}
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\centerline{\it Peking University and University of Hong Kong}
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\begin{quotation}
\noindent {\it Abstract:}
We examine the inference
problem of a proportional trapping model introduced by
Good, Lewis, Gaskins and Howell (1979), and consider a
similar removal model in
continuous time. The existence and uniqueness of the
maximum likelihood estimates of the parameters are studied.
Corresponding variance estimates are also
given.  Martingale theory is used to obtain the asymptotic properties, and
simulations are conducted to examine the performance of the estimation
procedure. \par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Counting process,  intensity function, martingale, proportional trapping.\par
\end{quotation}
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