Geodesic
On the distribution of the ratio of sums of random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 3, pp. 533-560

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We study the distribution of the ratio $Z_n$ of sums of random variables. Berry–Esseen-type estimates of the rate of convergence in the central limit theorem for $Z_n$ are given. In addition, second-order asymptotic expansions for $\mathbb E Z_n$ and $\mathbb E Z^2_n$ are presented. The results are applied to the problems of nonparametric regression curve estimation, nonparametric tail index estimation, and nonparametric estimation of a hazard function.
Keywords: Berry–Esseen-type estimates, tail index, hazard function, mean square error.
Mots-clés : regression 
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     author = {S. Yu. Novak},
     title = {On the distribution of the ratio of sums of random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {533--560},
     publisher = {mathdoc},
     volume = {41},
     number = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1996_41_3_a3/}
}
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S. Yu. Novak. On the distribution of the ratio of sums of random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 3, pp. 533-560. http://geodesic.mathdoc.fr/item/TVP_1996_41_3_a3/