Some results following from conditional characteristic functions

Yuan, De-Mei; Lei, Lan

doi:10.1080/03610926.2014.906614

Cited by 8 publications

(2 citation statements)

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“…The second concept is conditional symmetrization. Let X and X ′ be Findependent and F -identically distributed random variables, then X s F = X−X ′ is F -symmetric in view of Corollary 3.9 of Yuan and Lei [18] and we call X s F the F -symmetrization of X.…”

Section: Several Conditional Probability Inequalitiesmentioning

confidence: 99%

Convergence Rates for Sequences of Conditionally Independent and Conditionally Identically Distributed Random Variables

Yuan¹

2016

Journal of the Korean Mathematical Society

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Abstract. The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to (0, ∞) instead of (0, 2), we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.

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Section: Several Conditional Probability Inequalitiesmentioning

confidence: 99%

Convergence Rates for Sequences of Conditionally Independent and Conditionally Identically Distributed Random Variables

Yuan¹

2016

Journal of the Korean Mathematical Society

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“…Let us define for t ∈ R and ω ∈ Ω, Note that ϕ n is uniformly continuous on R almost surely, and since E[(W σ ) 2 |G] = 1, a.e., ϕ n is twice continuously differentiable almost surely. (SeeYuan and Lei (2016). )…”

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confidence: 99%

Stable limit theorems for empirical processes under conditional neighborhood dependence

Lee¹,

Song²

2019

Bernoulli

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This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets are indexed by the same set endowed with a neighborhood system. When the set of random variables satisfies CND, any two non-adjacent sets of random variables are conditionally independent given sigma algebras having indices in one of the two sets' neighborhood. Random variables with CND include those with conditional dependency graphs and a class of Markov random fields with a global Markov property. The CND property is useful for modeling cross-sectional dependence governed by a complex, large network. This paper provides two main results. The first result is a stable central limit theorem for a sum of random variables with CND. The second result is a Donsker-type result of stable convergence of empirical processes indexed by a class of functions satisfying a certain bracketing entropy condition when the random variables satisfy CND.

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