2003, Volume 65, Pt. 4 , 778--792

ASYMPTOTIC PROPERTIES OF THE MATCHES NUMBER IN PAIRING OBSERVATIONS

By

L.A. ZOLOTUKHINA and  A. YA. LINOV, State Marine Technical University, St. Petersburg, Russia

SUMMARY. The sample $(t_i,u_i) (i=1,2, \ldots, n)$ is extracted from two-dimensional population with probability  density $f(x,y)$.  The elements of every component are observed separately $\bar{t} =(t_1, t_2, \ldots, t_n)$ and $\bar{u} =(u_1, u_2, \ldots, u_n)$. In this paper we deduce an asymptotic formula for expected number of correct matches with an arbitrary method of initial sample reproducing. We provide a sufficient condition on the density $f(x,y)$ which ensures that natural matching is an asymptotically optimal method. We obtain integral representation of all matches number moments in the case of natural matching. We also prove that the asymptotic distribution of the matches number with natural matching is Poisson.

AMS (1991) subject classification. Primary 60G88; secondary 60F05.

Key words and phrases. Pairing observations, matching problem, Poisson approximation.

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