Weak and strong laws of large numbers for arrays of rowwise END random variables and their applications

Aiting Shen () and Andrei Volodin
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Aiting Shen: Anhui University
Andrei Volodin: University of Regina

Metrika: International Journal for Theoretical and Applied Statistics, 2017, vol. 80, issue 6, No 1, 605-625

Abstract: Abstract In the paper, the Marcinkiewicz–Zygmund type moment inequality for extended negatively dependent (END, in short) random variables is established. Under some suitable conditions of uniform integrability, the $$L_r$$ L r convergence, weak law of large numbers and strong law of large numbers for usual normed sums and weighted sums of arrays of rowwise END random variables are investigated by using the Marcinkiewicz–Zygmund type moment inequality. In addition, some applications of the $$L_r$$ L r convergence, weak and strong laws of large numbers to nonparametric regression models based on END errors are provided. The results obtained in the paper generalize or improve some corresponding ones for negatively associated random variables and negatively orthant dependent random variables.

Keywords: Extended negatively dependent random variables; $$L_r$$ L r convergence; Marcinkiewicz–Zygmund type moment inequality; Law of large numbers; Nonparametric regression models; 60F05; 60F15; 60F25; 62G05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-017-0618-z

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