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

João Lita da Silva

doi:10.1080/10485252.2019.1688326

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

João Lita da Silva

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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 {X_n,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 {b_n} 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 language	English
Pages (from-to)	20-41
Number of pages	22
Journal	Journal of Nonparametric Statistics
Volume	32
Issue number	1
DOIs	https://doi.org/10.1080/10485252.2019.1688326
Publication status	Published - 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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10.1080/10485252.2019.1688326

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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.",

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KW - widely orthant dependent random variables

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

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Keywords

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