Reduction principle for functionals of vector random fields

Olenko, Andriy; Omari, Dareen

doi:10.48550/arxiv.1803.11271

Cited by 2 publications

(5 citation statements)

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“…Note, that all assumptions of Theorem 1 in Olenko and Omari (2019) are satisfied in our case as α j = α, j = 1, . .…”

Section: Proofs Of the Results From Sectionmentioning

confidence: 99%

“…This approach can be extended to the case of random fields as Y (x) = η 1 (x)+ η2 (x), x ∈ R d , resulting in Y (x) with skewed marginal distributions. In the example below we use η2 (x) = η 2 2 (x) and show that contrary to the reduction principle for strongly dependent vector random fields in Olenko and Omari (2019)…”

Section: Reduction Principles and Limit Theoremsmentioning

confidence: 99%

“…The random variable K * r,l ≡ 0 if and only if l ∈ L + . Theorem 1 in Olenko and Omari (2019) gives a reduction principle for vector random fields with strongly dependent components. The following result complements it for the case of random fields with strongly and weakly dependent components.…”

Section: Reduction Principles and Limit Theoremsmentioning

confidence: 99%

“…The classical non-central limit theorems are based on another "proper" reduction principle, when the asymptotic behaviour is reduced only to the leading Hermite term of nonlinear functionals. Recently, Olenko and Omari (2019) proved the reduction principle for functionals of strongly dependent vector random fields. Components of such vector fields can possess different long-range dependences.…”

Section: Introductionmentioning

confidence: 99%

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Reduction principle for functionals of strong-weak dependent vector random fields

Olenko¹,

Omari²

2020

Braz. J. Probab. Stat.

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We prove the reduction principle for asymptotics of functionals of vector random fields with weakly and strongly dependent components. These functionals can be used to construct new classes of random fields with skewed and heavy-tailed distributions. Contrary to the case of scalar long-range dependent random fields, it is shown that the asymptotic behaviour of such functionals is not necessarily determined by the terms at their Hermite rank. The results are illustrated by an application to the first Minkowski functional of the Student random fields. Some simulation studies based on the theoretical findings are also presented.

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“…Note, that all assumptions of Theorem 1 in Olenko and Omari (2019) are satisfied in our case as α j = α, j = 1, . .…”

Section: Proofs Of the Results From Sectionmentioning

confidence: 99%

Section: Reduction Principles and Limit Theoremsmentioning

confidence: 99%

Section: Reduction Principles and Limit Theoremsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Reduction principle for functionals of strong-weak dependent vector random fields

Olenko¹,

Omari²

2020

Braz. J. Probab. Stat.

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“…It would be interesting to derive similar results for high frequency asymptotics where the observation window is the same but the sampling rate increases. Also, it would be important to obtain similar results for the case of functionals of vector data, see Olenko and Omari (2019).…”

Section: Multidimensional Casementioning

confidence: 99%

On asymptotics of discretized functionals of long-range dependent functional data

Alodat

Olenko

2020

Communications in Statistics - Theory and Methods

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The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given by these functionals. It is shown that in the discrete sampling case additive functionals have the same asymptotic distribution as the corresponding integral functionals for the continuous functional data case. These results are applied to obtain non-central limit theorems for weighted additive functionals of random fields. As the majority of known results concern the discrete sampling case the developed methodology helps in translating these results to functional data without deriving them again. Numerical studies suggest that the theoretical findings are valid for wider classes of long-range dependent data.

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Reduction principle for functionals of vector random fields

Cited by 2 publications

References 0 publications

Reduction principle for functionals of strong-weak dependent vector random fields

Reduction principle for functionals of strong-weak dependent vector random fields

On asymptotics of discretized functionals of long-range dependent functional data

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