Strong laws of large numbers for pairwise quadrant dependent random variables

João Lita da Silva

doi:10.1016/j.spl.2018.01.031

Strong laws of large numbers for pairwise quadrant dependent random variables

João Lita da Silva

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

3 Citations (Scopus)

Abstract

For a sequence {X_n,n⩾1} of quadrant dependent random variables satisfying EX_n<∞ for all n⩾1 and a family of positive sequences {b_n}, we give sufficient conditions to obtain ∑_k=1 ⁿ(X_k−EX_k)∕b_n⟶a.s.0. For random sequences which are additionally stochastically dominated by a random variable X∈ℒ_p, 1<p<2, we shall prove strong laws of large numbers under normalising sequences asymptotically equivalent to n^1∕p, 1<p<2 up to a logarithm power.

Original language	English
Pages (from-to)	349-358
Number of pages	10
Journal	Statistics and Probability Letters
Volume	137
DOIs	https://doi.org/10.1016/j.spl.2018.01.031
Publication status	Published - 1 Jun 2018

Keywords

Quadrant dependent random variables
Strong law of large numbers

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10.1016/j.spl.2018.01.031Licence: CC BY-NC-ND

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abstract = "For a sequence {Xn,n⩾1} of quadrant dependent random variables satisfying EXn<∞ for all n⩾1 and a family of positive sequences {bn}, we give sufficient conditions to obtain ∑k=1 n(Xk−EXk)∕bn⟶a.s.0. For random sequences which are additionally stochastically dominated by a random variable X∈ℒp, 11∕p, 1",

keywords = "Quadrant dependent random variables, Strong law of large numbers",

author = "{Lita da Silva}, Jo{\~a}o",

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N2 - For a sequence {Xn,n⩾1} of quadrant dependent random variables satisfying EXn<∞ for all n⩾1 and a family of positive sequences {bn}, we give sufficient conditions to obtain ∑k=1 n(Xk−EXk)∕bn⟶a.s.0. For random sequences which are additionally stochastically dominated by a random variable X∈ℒp, 11∕p, 1

AB - For a sequence {Xn,n⩾1} of quadrant dependent random variables satisfying EXn<∞ for all n⩾1 and a family of positive sequences {bn}, we give sufficient conditions to obtain ∑k=1 n(Xk−EXk)∕bn⟶a.s.0. For random sequences which are additionally stochastically dominated by a random variable X∈ℒp, 11∕p, 1

KW - Quadrant dependent random variables

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JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

ER -

Strong laws of large numbers for pairwise quadrant dependent random variables

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Keywords

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