A goodness-of-fit test for inhomogeneous spatial Poisson processes

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We introduce a formal testing procedure to assess the fit of an inhomogeneous spatial Poisson process model, based on a discrepancy measure function that is constructed from residuals obtained from the fitted model. We derive the asymptotic distributional properties of and develop a test statistic based on them. Our test statistic has a limiting standard normal distribution, so that the test can be performed by simply comparing the test statistic with readily available critical values. We perform a simulation study to assess the performance of the proposed method and apply it to a real data example.

Original languageEnglish (US)
Pages (from-to)831-845
Number of pages15
JournalBiometrika
Volume95
Issue number4
DOIs
StatePublished - Dec 2008
Externally publishedYes

Fingerprint

Spatial Process
Goodness of Fit Test
Poisson process
Test Statistic
Statistics
statistics
Standard Normal distribution
Normal Distribution
Poisson Model
testing
Normal distribution
Process Model
Discrepancy
Critical value
Limiting
Simulation Study
Model-based
Testing
Test statistic
Goodness of fit test

Keywords

  • Goodness-of-fit test
  • Inhomogeneous spatial Poisson process
  • Residual diagnostic

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Statistics, Probability and Uncertainty
  • Mathematics(all)
  • Applied Mathematics
  • Statistics and Probability

Cite this

A goodness-of-fit test for inhomogeneous spatial Poisson processes. / Guan, Yongtao.

In: Biometrika, Vol. 95, No. 4, 12.2008, p. 831-845.

Research output: Contribution to journalArticle

@article{1fd273df358741c294b193cfec6e3ab5,
title = "A goodness-of-fit test for inhomogeneous spatial Poisson processes",
abstract = "We introduce a formal testing procedure to assess the fit of an inhomogeneous spatial Poisson process model, based on a discrepancy measure function that is constructed from residuals obtained from the fitted model. We derive the asymptotic distributional properties of and develop a test statistic based on them. Our test statistic has a limiting standard normal distribution, so that the test can be performed by simply comparing the test statistic with readily available critical values. We perform a simulation study to assess the performance of the proposed method and apply it to a real data example.",
keywords = "Goodness-of-fit test, Inhomogeneous spatial Poisson process, Residual diagnostic",
author = "Yongtao Guan",
year = "2008",
month = "12",
doi = "10.1093/biomet/asn045",
language = "English (US)",
volume = "95",
pages = "831--845",
journal = "Biometrika",
issn = "0006-3444",
publisher = "Oxford University Press",
number = "4",

}

TY - JOUR

T1 - A goodness-of-fit test for inhomogeneous spatial Poisson processes

AU - Guan, Yongtao

PY - 2008/12

Y1 - 2008/12

N2 - We introduce a formal testing procedure to assess the fit of an inhomogeneous spatial Poisson process model, based on a discrepancy measure function that is constructed from residuals obtained from the fitted model. We derive the asymptotic distributional properties of and develop a test statistic based on them. Our test statistic has a limiting standard normal distribution, so that the test can be performed by simply comparing the test statistic with readily available critical values. We perform a simulation study to assess the performance of the proposed method and apply it to a real data example.

AB - We introduce a formal testing procedure to assess the fit of an inhomogeneous spatial Poisson process model, based on a discrepancy measure function that is constructed from residuals obtained from the fitted model. We derive the asymptotic distributional properties of and develop a test statistic based on them. Our test statistic has a limiting standard normal distribution, so that the test can be performed by simply comparing the test statistic with readily available critical values. We perform a simulation study to assess the performance of the proposed method and apply it to a real data example.

KW - Goodness-of-fit test

KW - Inhomogeneous spatial Poisson process

KW - Residual diagnostic

UR - http://www.scopus.com/inward/record.url?scp=57249090983&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57249090983&partnerID=8YFLogxK

U2 - 10.1093/biomet/asn045

DO - 10.1093/biomet/asn045

M3 - Article

AN - SCOPUS:57249090983

VL - 95

SP - 831

EP - 845

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 4

ER -