Geodesic
Convergence of random sequences with independent random indices.~II
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 907-910

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Necessary and sufficient conditions are obtained for the convergence of some statistics constructed from samples with random sizes.
Keywords: random sequences with random indices, weak convergence, samples with random sizes, order statistics, asymptotically normal statistics. 
@article{TVP_1995_40_4_a18,
     author = {V. Yu. Korolev},
     title = {Convergence of random sequences with independent random {indices.~II}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {907--910},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a18/}
}
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V. Yu. Korolev. Convergence of random sequences with independent random indices.~II. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 907-910. http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a18/