Limit Theorems for Associated Random Fields and Related Systems

Bulinski, Alexander; Shashkin, A. P.

doi:10.1142/6555

Cited by 134 publications

(148 citation statements)

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“…For basic results on associated random variables, please refer to the monographs Bulinski, Shashkin [4], Oliveira [22] or Prakasa Rao [26]. It is well known that the covariance structure of associated random variables characterizes their asymptotics, so it is natural to seek assumptions on the covariances.…”

Section: Framework and Auxiliary Resultsmentioning

confidence: 99%

A moderate deviation for associated random variables

Çağın

Oliveira

Torrado

2016

Journal of the Korean Statistical Society

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Moderate deviations are an important topic in many theoretical or applied statistical areas. We prove two versions of a moderate deviation for associated and strictly stationary random variables with finite moments of order q > 2. The first one uses an assumption depending on the rate of a Gaussian approximation, while the second one discusses more natural assumptions to obtain the approximation rate. The control of the dependence structure relies on the decay rate of the covariances, for which we assume a relatively mild polynomial decay rate. The proof combines a coupling argument together with a suitable use of Berry-Esséen bounds.

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Section: Framework and Auxiliary Resultsmentioning

confidence: 99%

A moderate deviation for associated random variables

Çağın

Oliveira

Torrado

2016

Journal of the Korean Statistical Society

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“…We also assume that X is square integrable and its covariance function r(t) = Cov(X 0 , X t ), t ∈ R d , is continuous. Note that due to the latter condition X is also associated (see [10] for the definition of association and related dependence types).…”

Section: Central Limit Theoremmentioning

confidence: 99%

A Central Limit Theorem for the Volumes of High Excursions of Stationary Associated Random Fields

Demichev

Olszewski

2015

Stat., optim. inf. comput.

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“…We would also like to refer the reader to the monograph [2], where the covariance inequalities for Lipschitz functions of associated r.v. 's are studied.…”

Section: It Is Easy To See That Cov I (−∞T (X ) I (−∞S (Y ) = H Xmentioning

confidence: 99%

“…Several limit theorems have been proved under this kind of dependence, in particular: laws of large numbers, CLT and the rate of convergence in the CLT, invariance principle, moment bounds, convergence of empirical processes etc. (see [2,10,11] where further references are given). Now let X, Y be any random variables and X , Y independent copies of X and Y , i.e.…”

Section: It Is Easy To See That Cov I (−∞T (X ) I (−∞S (Y ) = H Xmentioning

confidence: 99%