Geodesic
Estimation in the Markov-P\'olya scheme
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 373-382

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The Markov-Pólya urn scheme is considered, in which the balls are sequentially and equiprobably drawn from an urn initially containing a given number $a_j$ of balls of the $j$th color, $j=1,\dots,N$, and after each draw the ball is returned into the urn together with $s$ new balls of the same color. It is assumed that at the beginning only the total number of balls in the urn is known and one must estimate its structure $\overline\theta=(\theta_1,\dots,\theta_N)$ by observing the frequencies in $n$ trials of the balls of corresponding colors. Various approaches including the Bayes and minimax ones for estimating $\overline\theta$ under a quadratic loss function are discussed. The connection of the obtained results with known ones for multinomial and multivariate hypergeometric distributions is also discussed. 
@article{MZM_1998_64_3_a4,
     author = {G. I. Ivchenko},
     title = {Estimation in the {Markov-P\'olya} scheme},
     journal = {Matemati\v{c}eskie zametki},
     pages = {373--382},
     publisher = {mathdoc},
     volume = {64},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a4/}
}
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G. I. Ivchenko. Estimation in the Markov-P\'olya scheme. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 373-382. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a4/