Abstract
This paper discusses a new perspective in fitting spatial point process models. Specifically the spatial point process of interest is treated as a marked point process where at each observed event x a stochastic process M (x ; t), 0 < t < r, is defined. Each mark process M (x ; t) is compared with its expected value, say F (t ; θ), to produce a discrepancy measure at x, where θ is a set of unknown parameters. All individual discrepancy measures are combined to define an overall measure which will then be minimized to estimate the unknown parameters. The proposed approach can be easily applied to data with sample size commonly encountered in practice. Simulations and an application to a real data example demonstrate the efficacy of the proposed approach.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2143-2153 |
| Number of pages | 11 |
| Journal | Journal of Statistical Planning and Inference |
| Volume | 138 |
| Issue number | 7 |
| DOIs | |
| State | Published - Jul 1 2008 |
| Externally published | Yes |
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Keywords
- K-function
- Marked point process
- Spatial point process
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability
Cite this
A marked point process perspective in fitting spatial point process models. / Guan, Yongtao.
In: Journal of Statistical Planning and Inference, Vol. 138, No. 7, 01.07.2008, p. 2143-2153.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A marked point process perspective in fitting spatial point process models
AU - Guan, Yongtao
PY - 2008/7/1
Y1 - 2008/7/1
N2 - This paper discusses a new perspective in fitting spatial point process models. Specifically the spatial point process of interest is treated as a marked point process where at each observed event x a stochastic process M (x ; t), 0 < t < r, is defined. Each mark process M (x ; t) is compared with its expected value, say F (t ; θ), to produce a discrepancy measure at x, where θ is a set of unknown parameters. All individual discrepancy measures are combined to define an overall measure which will then be minimized to estimate the unknown parameters. The proposed approach can be easily applied to data with sample size commonly encountered in practice. Simulations and an application to a real data example demonstrate the efficacy of the proposed approach.
AB - This paper discusses a new perspective in fitting spatial point process models. Specifically the spatial point process of interest is treated as a marked point process where at each observed event x a stochastic process M (x ; t), 0 < t < r, is defined. Each mark process M (x ; t) is compared with its expected value, say F (t ; θ), to produce a discrepancy measure at x, where θ is a set of unknown parameters. All individual discrepancy measures are combined to define an overall measure which will then be minimized to estimate the unknown parameters. The proposed approach can be easily applied to data with sample size commonly encountered in practice. Simulations and an application to a real data example demonstrate the efficacy of the proposed approach.
KW - K-function
KW - Marked point process
KW - Spatial point process
UR - http://www.scopus.com/inward/record.url?scp=40949131814&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=40949131814&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2007.09.008
DO - 10.1016/j.jspi.2007.09.008
M3 - Article
AN - SCOPUS:40949131814
VL - 138
SP - 2143
EP - 2153
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
SN - 0378-3758
IS - 7
ER -