Nonparametric indices of dependence between components for inhomogeneous multivariate random measures and marked sets

Maria Nicolette Margaretha van Lieshout

doi:10.1111/sjos.12331

Nonparametric indices of dependence between components for inhomogeneous multivariate random measures and marked sets

Maria Nicolette Margaretha van Lieshout (Corresponding Author)

Stochastic Operations Research

Research output: Contribution to journal › Article › Academic › peer-review

6 Citations (Scopus)

113 Downloads (Pure)

Abstract

We propose new summary statistics to quantify the association between the components in coverage-reweighted moment stationary multivariate random sets and measures. They are defined in terms of the coverage-reweighted cumulant densities and extend classic functional statistics for stationary random closed sets. We study the relations between these statistics and evaluate them explicitly for a range of models. Unbiased estimators are given for all statistics and applied to simulated examples and to tropical rain forest data.

Original language	English
Pages (from-to)	985-1015
Number of pages	31
Journal	Scandinavian journal of statistics
Volume	45
Issue number	4
DOIs	https://doi.org/10.1111/sjos.12331
Publication status	Published - 8 Mar 2018

Keywords

UT-Hybrid-D
Coverage-reweighted moment stationarity
Cross hitting functional
Empty space function
J-function,
K-function,
Moment measure
Reduced cross correlation measure
Spherical contact distribution
Bivariate random measure

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10.1111/sjos.12331Licence: CC BY

2018-XLieshout_Scandinavian_Journal_of_StatisticsFinal published version, 1.43 MBLicence: CC BY

Cite this

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title = "Nonparametric indices of dependence between components for inhomogeneous multivariate random measures and marked sets",

abstract = "We propose new summary statistics to quantify the association between the components in coverage-reweighted moment stationary multivariate random sets and measures. They are defined in terms of the coverage-reweighted cumulant densities and extend classic functional statistics for stationary random closed sets. We study the relations between these statistics and evaluate them explicitly for a range of models. Unbiased estimators are given for all statistics and applied to simulated examples and to tropical rain forest data.",

keywords = "UT-Hybrid-D, Coverage-reweighted moment stationarity, Cross hitting functional, Empty space function, J-function,, K-function,, Moment measure, Reduced cross correlation measure, Spherical contact distribution, Bivariate random measure",

author = "{van Lieshout}, {Maria Nicolette Margaretha}",

note = "Wiley deal †In memory of J. Oosterhoff. ",

year = "2018",

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doi = "10.1111/sjos.12331",

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T1 - Nonparametric indices of dependence between components for inhomogeneous multivariate random measures and marked sets

AU - van Lieshout, Maria Nicolette Margaretha

N1 - Wiley deal †In memory of J. Oosterhoff.

PY - 2018/3/8

Y1 - 2018/3/8

N2 - We propose new summary statistics to quantify the association between the components in coverage-reweighted moment stationary multivariate random sets and measures. They are defined in terms of the coverage-reweighted cumulant densities and extend classic functional statistics for stationary random closed sets. We study the relations between these statistics and evaluate them explicitly for a range of models. Unbiased estimators are given for all statistics and applied to simulated examples and to tropical rain forest data.

AB - We propose new summary statistics to quantify the association between the components in coverage-reweighted moment stationary multivariate random sets and measures. They are defined in terms of the coverage-reweighted cumulant densities and extend classic functional statistics for stationary random closed sets. We study the relations between these statistics and evaluate them explicitly for a range of models. Unbiased estimators are given for all statistics and applied to simulated examples and to tropical rain forest data.

KW - UT-Hybrid-D

KW - Coverage-reweighted moment stationarity

KW - Cross hitting functional

KW - Empty space function

KW - J-function,

KW - K-function,

KW - Moment measure

KW - Reduced cross correlation measure

KW - Spherical contact distribution

KW - Bivariate random measure

U2 - 10.1111/sjos.12331

DO - 10.1111/sjos.12331

M3 - Article

SN - 0303-6898

VL - 45

SP - 985

EP - 1015

JO - Scandinavian journal of statistics

JF - Scandinavian journal of statistics

IS - 4

ER -

Nonparametric indices of dependence between components for inhomogeneous multivariate random measures and marked sets

Abstract

Keywords

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