Planar segment processes with reference mark distributions, modeling and estimation

Beneš, Viktor; Vecera, Jakub; Pultar, Milan

doi:10.48550/arxiv.1701.01893

Search citation statements

Order By: Relevance

Paper Sections

Select...

Infinite Volume Gibbs Particle Process1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

Publication Types

Select...

Other1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has to be mentioned that the reference distribution Q need not coincide with the observed joint length-direction distribution of the process, cf. [1].…”

Section: Infinite Volume Gibbs Particle Processmentioning

confidence: 99%

See 1 more Smart Citation

Gaussian approximation for functionals of Gibbs particle processes

Novotna¹,

Beneš²

2017

Preprint

Self Cite

View full text Add to dashboard Cite

In the paper asymptotic properties of functionals of stationary Gibbs particle processes are derived. Two known techniques from the point process theory in the Euclidean space R d are extended to the space of compact sets on R d equipped with the Hausdorff metric. First, conditions for the existence of the stationary Gibbs point process with given conditional intensity have been simplified recently. Secondly, the Malliavin-Stein method was applied to the estimation of Wasserstein distance between the Gibbs input and standard Gaussian distribution. We transform these theories to the space of compact sets and use them to derive a Gaussian approximation for functionals of a planar Gibbs segment process.

show abstract

“…It has to be mentioned that the reference distribution Q need not coincide with the observed joint length-direction distribution of the process, cf. [1].…”

Section: Infinite Volume Gibbs Particle Processmentioning

confidence: 99%

“…[1], therefore using (3) we can choose b = a(2R) d ω d , where ω d is the volume of the unit ball in R d . The upper bound follows from(12).…”

mentioning

confidence: 99%