Recent zbMATH articles in MSC 60B12
https://zbmath.org/atom/cc/60B12
2021-06-15T18:09:00+00:00
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Mathematical foundations of infinite-dimensional statistical models. Revised paperback edition.
https://zbmath.org/1460.62007
2021-06-15T18:09:00+00:00
"GinĂ©, Evarist"
https://zbmath.org/authors/?q=ai:gine.evarist
"Nickl, Richard"
https://zbmath.org/authors/?q=ai:nickl.richard
See the review of the hardback edition in [Zbl 1358.62014].
On the strong law of large numbers for linear combinations of concomitants.
https://zbmath.org/1460.62062
2021-06-15T18:09:00+00:00
"Dudkina, O. I."
https://zbmath.org/authors/?q=ai:dudkina.o-i
"Gribkova, N. V."
https://zbmath.org/authors/?q=ai:gribkova.nadezhda-v
Summary: A theorem on the strong law of large numbers for linear functions of concomitants (induced order statistics) for sequences of independent identically distributed two-dimensional random vectors is proved in this paper. The result complements previous work by \textit{S.-S. Yang} [Ann. Inst. Stat. Math. 33, 463--470 (1981; Zbl 0478.62036)] and the second author with \textit{R. Zitikis} [Math. Methods Stat. 26, No. 4, 267--281 (2017; Zbl 06845133); Ann. Inst. Stat. Math. 71, No. 4, 811--835 (2019; Zbl 1433.62295)]. The proof is based on the conditional independence property of the concomitants established by \textit{P. K. Bhattacharya} [Ann. Stat. 2, 1034--1039 (1974; Zbl 0307.62036)]; the \textit{W. R. van Zwet} strong law of large numbers for linear functions of order statistics [Ann. Probab. 8, 986--990 (1980; Zbl 0448.60025)] is used and classical inequalities apply, including the \textit{H. P. Rosenthal} inequality [Isr. J. Math. 8, 273--303 (1970; Zbl 0213.19303)].