On least squares fitting for stationary spatial point processes

Yongtao Guan, Michael Sherman

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The K-function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability. In this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the K-function by using subsampling. We demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures. This is done through asymptotic theory, simulation experiments and an application to a data set on long leaf pine-trees.

Original languageEnglish (US)
Pages (from-to)31-49
Number of pages19
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume69
Issue number1
DOIs
StatePublished - Feb 2007
Externally publishedYes

Fingerprint

Spatial Point Process
Least Square Fitting
Subsampling
Model Fitting
Least Squares Estimator
Asymptotic Theory
Asymptotic Normality
Process Model
Simulation Experiment
Simplicity
Leaves
Estimator
Model
Demonstrate
Point process
Least squares

Keywords

  • K-function
  • Least squares estimator
  • Spatial point process
  • Subsampling

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

On least squares fitting for stationary spatial point processes. / Guan, Yongtao; Sherman, Michael.

In: Journal of the Royal Statistical Society. Series B: Statistical Methodology, Vol. 69, No. 1, 02.2007, p. 31-49.

Research output: Contribution to journalArticle

@article{fa32d8e46dcf4ebfbf447bed2fe8e285,
title = "On least squares fitting for stationary spatial point processes",
abstract = "The K-function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability. In this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the K-function by using subsampling. We demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures. This is done through asymptotic theory, simulation experiments and an application to a data set on long leaf pine-trees.",
keywords = "K-function, Least squares estimator, Spatial point process, Subsampling",
author = "Yongtao Guan and Michael Sherman",
year = "2007",
month = "2",
doi = "10.1111/j.1467-9868.2007.00575.x",
language = "English (US)",
volume = "69",
pages = "31--49",
journal = "Journal of the Royal Statistical Society. Series B: Statistical Methodology",
issn = "1369-7412",
publisher = "Wiley-Blackwell",
number = "1",

}

TY - JOUR

T1 - On least squares fitting for stationary spatial point processes

AU - Guan, Yongtao

AU - Sherman, Michael

PY - 2007/2

Y1 - 2007/2

N2 - The K-function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability. In this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the K-function by using subsampling. We demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures. This is done through asymptotic theory, simulation experiments and an application to a data set on long leaf pine-trees.

AB - The K-function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability. In this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the K-function by using subsampling. We demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures. This is done through asymptotic theory, simulation experiments and an application to a data set on long leaf pine-trees.

KW - K-function

KW - Least squares estimator

KW - Spatial point process

KW - Subsampling

UR - http://www.scopus.com/inward/record.url?scp=33846194044&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846194044&partnerID=8YFLogxK

U2 - 10.1111/j.1467-9868.2007.00575.x

DO - 10.1111/j.1467-9868.2007.00575.x

M3 - Article

AN - SCOPUS:33846194044

VL - 69

SP - 31

EP - 49

JO - Journal of the Royal Statistical Society. Series B: Statistical Methodology

JF - Journal of the Royal Statistical Society. Series B: Statistical Methodology

SN - 1369-7412

IS - 1

ER -