Weak laws of large numbers for maximal weighted sums of random variables. (English) Zbl 07532108
Summary: In this paper, we establish a weak law of large numbers for a class of weighted sums of random variables introduced by R. Jajte [Ann. Probab. 31, No. 1, 409–412 (2003; Zbl 1013.60021)]. The obtained method allows us to deduce a generalized version of the Marcinkiewicz-Zygmund weak law of large numbers and to strengthen several known results, such as those of A. Gut [J. Theor. Probab. 17, No. 3, 769–779 (2004; Zbl 1064.60037)] and H. Naderi et al. [Commun. Stat., Theory Methods 48, No. 21, 5414–5418 (2019; Zbl 07529863)]. Finally, an application to randomly indexed sums is presented.
MSC:
| 60F15 | Strong limit theorems |
| 60G50 | Sums of independent random variables; random walks |
| 62-XX | Statistics |
Keywords:
Kolmogorov-Feller weak law; weighted averages; maximal inequalities; Marcinkiewicz-Zygmund weak law; limit theoremsReferences:
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