Asymptotic Approximations of Ratio Moments Based on Dependent Sequences

Fang, Hongyan; Ding, Saisai; Li, Xiaoqin; Yang, Wenzhi

doi:10.3390/math8030361

Cited by 7 publications

(12 citation statements)

References 38 publications

(68 reference statements)

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“…The results obtained by this paper and Fang et al [19] are different. In our paper, we mainly discuss the complete moment convergence of moving average processes for an m-WOD sequence, Fang et al [19] proved the asymptotic approximations of ratio moments based on the m-WOD sequence.…”

Section: Remark 37contrasting

confidence: 85%

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Complete moment convergence of moving average processes for m-WOD sequence

2021

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In this paper, the complete moment convergence for the partial sum of moving average processes $\{X_{n}=\sum_{i=-\infty }^{\infty }a_{i}Y_{i+n},n\geq 1\}$ { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } is established under some mild conditions, where $\{Y_{i},-\infty < i<\infty \}$ { Y i , − ∞ < i < ∞ } is a sequence of m-widely orthant dependent (m-WOD, for short) random variables which is stochastically dominated by a random variable Y, and $\{a_{i},-\infty < i<\infty \}$ { a i , − ∞ < i < ∞ } is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results from m-extended negatively dependent (m-END, for short) sequences to m-WOD sequences.

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Section: Remark 37contrasting

confidence: 85%

“…If {f n (•), n ≥ 1} are all nondecreasing (or nonincreasing), then {f n (X n ), n ≥ 1} are still m-WOD with dominating coefficients {g(n), n ≥ 1}. Lemma 2.2 (Fang et al [19]) For a positive real number q ≥ 2, if {X n , n ≥ 1} is a sequence of mean zero m-WOD random variables with dominating coefficients g…”

Section: Preliminary Lemmasmentioning

confidence: 99%

Complete moment convergence of moving average processes for m-WOD sequence

2021

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“…The random variables {X n n ≥ 1} are said to be WOD random variables, if the random variables {X n n ≥ 1} are both WUOD and WLOD, g(n) = max{g U (n)g L (n)} Inspired by m-NA and WOD, the concept of m-WOD random variables was introduced by Fang et al [2] , as follows:…”

Section: Definitionmentioning

confidence: 99%

Complete qth-Moment Convergence of Moving Average Process for m-WOD Random Variable

Song

CHU

2022

Wuhan Univ. J. Nat. Sci.

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In this paper, we obtained complete qth-moment convergence of the moving average processes, which is generated by m-WOD moving random variables. The results in this article improve and extend the results of the moving average process. m-WOD random variables include WOD, m-NA, m-NOD and m-END random variables, so the results in the paper also promote the corresponding ones in WOD, m-NA, m-NOD, m-END random variables .

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“…For more about copulas applications in problems related to modelling dependence of heavy-tailed distributions, the reader may refer to the works of Albrechter et al [41], Asimit et al [22], Fang et al [42], Yang et al [43] and Wang et al [24] (and the references therein). For a systematic treatment of copulas theory see, for instance, the work of Nelsen [38].…”

Section: Qai Dependence Structurementioning

confidence: 99%

Tails of the Moments for Sums with Dominatedly Varying Random Summands

2021

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The asymptotic behaviour of the tail expectation ?E(Snξ)α?{Snξ>x} is investigated, where exponent α is a nonnegative real number and Snξ=ξ1+…+ξn is a sum of dominatedly varying and not necessarily identically distributed random summands, following a specific dependence structure. It turns out that the tail expectation of such a sum can be asymptotically bounded from above and below by the sums of expectations ?Eξiα?{ξi>x} with correcting constants. The obtained results are extended to the case of randomly weighted sums, where collections of random weights and primary random variables are independent. For illustration of the results obtained, some particular examples are given, where dependence between random variables is modelled in copulas framework.

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Asymptotic Approximations of Ratio Moments Based on Dependent Sequences

Cited by 7 publications

References 38 publications

Complete moment convergence of moving average processes for m-WOD sequence

Complete moment convergence of moving average processes for m-WOD sequence

Complete qth-Moment Convergence of Moving Average Process for m-WOD Random Variable

Tails of the Moments for Sums with Dominatedly Varying Random Summands

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