### Abstract

Ecological data often involve measurements taken at irregularly spaced locations (e.g., the heights of trees in a forest). A useful approach for modeling such data is via a marked point process, where the marks (i.e., measurements) and points (i.e., locations) are often assumed to be independent. Although this is a convenient assumption, it may not hold in practice. Schlather et al. (Journal of the Royal Statistical Society Services B, 66, 79-93, 2004) proposed a simulation-based approach to test this assumption. This paper presents a new method for testing the assumption of independence between the marks and the points. Instead of considering a simulation approach, we derive analytical results that allow the test to be implemented via a conventional χ^{2} statistic. We illustrate the use of our approach by applying it to an example involving desert plant data.

Original language | English (US) |
---|---|

Pages (from-to) | 101-111 |

Number of pages | 11 |

Journal | Environmental and Ecological Statistics |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

- Conditional expectation of marks
- Subsampling

### ASJC Scopus subject areas

- Environmental Science(all)
- Environmental Chemistry

### Cite this

*Environmental and Ecological Statistics*,

*14*(2), 101-111. https://doi.org/10.1007/s10651-007-0010-7

**Test for independence between marks and points of marked point processes : A subsampling approach.** / Guan, Yongtao; Afshartous, David R.

Research output: Contribution to journal › Article

*Environmental and Ecological Statistics*, vol. 14, no. 2, pp. 101-111. https://doi.org/10.1007/s10651-007-0010-7

}

TY - JOUR

T1 - Test for independence between marks and points of marked point processes

T2 - A subsampling approach

AU - Guan, Yongtao

AU - Afshartous, David R.

PY - 2007/6

Y1 - 2007/6

N2 - Ecological data often involve measurements taken at irregularly spaced locations (e.g., the heights of trees in a forest). A useful approach for modeling such data is via a marked point process, where the marks (i.e., measurements) and points (i.e., locations) are often assumed to be independent. Although this is a convenient assumption, it may not hold in practice. Schlather et al. (Journal of the Royal Statistical Society Services B, 66, 79-93, 2004) proposed a simulation-based approach to test this assumption. This paper presents a new method for testing the assumption of independence between the marks and the points. Instead of considering a simulation approach, we derive analytical results that allow the test to be implemented via a conventional χ2 statistic. We illustrate the use of our approach by applying it to an example involving desert plant data.

AB - Ecological data often involve measurements taken at irregularly spaced locations (e.g., the heights of trees in a forest). A useful approach for modeling such data is via a marked point process, where the marks (i.e., measurements) and points (i.e., locations) are often assumed to be independent. Although this is a convenient assumption, it may not hold in practice. Schlather et al. (Journal of the Royal Statistical Society Services B, 66, 79-93, 2004) proposed a simulation-based approach to test this assumption. This paper presents a new method for testing the assumption of independence between the marks and the points. Instead of considering a simulation approach, we derive analytical results that allow the test to be implemented via a conventional χ2 statistic. We illustrate the use of our approach by applying it to an example involving desert plant data.

KW - Conditional expectation of marks

KW - Subsampling

UR - http://www.scopus.com/inward/record.url?scp=34250011252&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250011252&partnerID=8YFLogxK

U2 - 10.1007/s10651-007-0010-7

DO - 10.1007/s10651-007-0010-7

M3 - Article

AN - SCOPUS:34250011252

VL - 14

SP - 101

EP - 111

JO - Environmental and Ecological Statistics

JF - Environmental and Ecological Statistics

SN - 1352-8505

IS - 2

ER -