Unusual strong laws for arrays of ratios of order statistics
Adler, André
Braz. J. Probab. Stat., Tome 25 (2011) no. 1, p. 34-43 / Harvested from Project Euclid
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Let {Xn, k, 1 ≤ k ≤ mn, n ≥ 1} be independent random variables from the Pareto distribution. Let Xn(k) be the kth largest order statistic from the nth row of our array, where Xn(1) denotes the largest order statistic from the nth row. Then set Rn, in, jn = Xn(jn) / Xn(in) where jn < in. This paper establishes limit theorems involving weighted sums from the sequence {Rn, in, jn, n ≥ 1}, where for the first time we allow jn → ∞, but only at a slow rate.
Publié le : 2011-03-15
Classification:  Almost sure convergence,  strong law of large numbers 
@article{1291387772,
     author = {Adler, Andr\'e},
     title = {Unusual strong laws for arrays of ratios of order statistics},
     journal = {Braz. J. Probab. Stat.},
     volume = {25},
     number = {1},
     year = {2011},
     pages = { 34-43},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1291387772}
}

Adler, André. Unusual strong laws for arrays of ratios of order statistics. Braz. J. Probab. Stat., Tome 25 (2011) no. 1, pp.  34-43. http://gdmltest.u-ga.fr/item/1291387772/