Strong laws of large numbers for arrays of row-wise extended negatively dependent random variables with applications

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Abstract

The main purpose of this paper is to obtain strong laws of large numbers for arrays or weighted sums of random variables under a scenario of dependence. Namely, for triangular arrays {Xn,j, 1 ≤ j ≤ n, n ≥ 1} of row-wise extended negatively dependent random variables weakly mean dominated by a random variable X ϵ L1 and sequences {bn} of positive constants, conditions are given to ensure (Formula presented.). Our statements allow us to establish strong consistency of general nonparametric estimates in a nonparametric regression model having fixed design points.

Original languageEnglish
Pages (from-to)20-41
Number of pages22
JournalJournal of Nonparametric Statistics
Volume32
Issue number1
DOIs
Publication statusPublished - 2 Jan 2020

Keywords

  • Bennett inequality
  • nonparametric estimation
  • Row-wise extended negatively dependent arrays
  • strong consistency
  • strong laws of large numbers
  • widely orthant dependent random variables

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