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Goodness-of-fit test for point processes first-order intensity

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  • Borrajo, M.I.
  • González-Manteiga, W.
  • Martínez-Miranda, M.D.

Abstract

Modelling the first-order intensity function is one of the main aims in point process theory. An appropriate model describes the first-order intensity as a nonparametric function of spatial covariates. A formal testing procedure is presented to assess the goodness-of-fit of this model, assuming an inhomogeneous Poisson point process. The test is based on a quadratic distance between two kernel intensity estimators. The asymptotic normality of the test statistic is proved and a bootstrap procedure to approximate its distribution is suggested. The proposal is illustrated with two applications to real data sets, and an extensive simulation study to evaluate its finite-sample performance.

Suggested Citation

  • Borrajo, M.I. & González-Manteiga, W. & Martínez-Miranda, M.D., 2024. "Goodness-of-fit test for point processes first-order intensity," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:csdana:v:194:y:2024:i:c:s0167947324000136
    DOI: 10.1016/j.csda.2024.107929
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    References listed on IDEAS

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    1. Guan, Yongtao & Loh, Ji Meng, 2007. "A Thinned Block Bootstrap Variance Estimation Procedure for Inhomogeneous Spatial Point Patterns," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1377-1386, December.
    2. Cao, R., 1993. "Bootstrapping the Mean Integrated Squared Error," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 137-160, April.
    3. Rob Foxall & Adrian Baddeley, 2002. "Nonparametric measures of association between a spatial point process and a random set, with geological applications," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(2), pages 165-182, May.
    4. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 442-447, September.
    5. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    6. Hyndman, R.J. & Yao, Q., 1998. "Nonparametric Estimation and Symmetry Tests for Conditional Density Functions," Monash Econometrics and Business Statistics Working Papers 17/98, Monash University, Department of Econometrics and Business Statistics.
    7. Baddeley, Adrian & Hardegen, Andrew & Lawrence, Thomas & Milne, Robin K. & Nair, Gopalan & Rakshit, Suman, 2017. "On two-stage Monte Carlo tests of composite hypotheses," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 75-87.
    8. J. Chacón & T. Duong, 2010. "Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 375-398, August.
    9. Borrajo, M.I. & González-Manteiga, W. & Martínez-Miranda, M.D., 2020. "Bootstrapping kernel intensity estimation for inhomogeneous point processes with spatial covariates," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. P. J. Diggle & V. Gómez-Rubio & P. E. Brown & A. G. Chetwynd & S. Gooding, 2007. "Second-Order Analysis of Inhomogeneous Spatial Point Processes Using Case–Control Data," Biometrics, The International Biometric Society, vol. 63(2), pages 550-557, June.
    11. Peter Diggle, 1985. "A Kernel Method for Smoothing Point Process Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(2), pages 138-147, June.
    12. Guan, Yongtao, 2008. "On Consistent Nonparametric Intensity Estimation for Inhomogeneous Spatial Point Processes," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1238-1247.
    13. Rasmus Plenge Waagepetersen, 2007. "An Estimating Function Approach to Inference for Inhomogeneous Neyman–Scott Processes," Biometrics, The International Biometric Society, vol. 63(1), pages 252-258, March.
    14. Yongtao Guan & Ye Shen, 2010. "A weighted estimating equation approach for inhomogeneous spatial point processes," Biometrika, Biometrika Trust, vol. 97(4), pages 867-880.
    15. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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