Weighted version of strong law of large numbers for a class of random variables and its applications

Yi Wu (), Xuejun Wang (), Shuhe Hu () and Lianqiang Yang ()
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Yi Wu: Anhui University
Xuejun Wang: Anhui University
Shuhe Hu: Anhui University
Lianqiang Yang: Anhui University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 2, No 7, 379-406

Abstract: Abstract In this paper, the single index weighted version of Marcinkiewicz–Zygmund type strong law of large numbers and the double index weighted version of Marcinkiewicz–Zygmund type strong law of large numbers are investigated successively for a class of random variables, which extends the classical results for independent and identically distributed random variables. As applications of the results, we further study the strong consistency for the weighted estimator in the nonparametric regression model and the least square estimators in the simple linear errors-in-variables model. Moreover, we also present some numerical study to verify the validity of our results.

Keywords: Strong law of large numbers; Rosenthal-type inequality; Double index weight; Nonparametric regression model; Simple linear errors-in-variables model; Strong consistency; 60F15; 62G05; 62G20 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11749-017-0550-6

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