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Second‐order residual analysis of spatiotemporal point processes and applications in model evaluation

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  • Jiancang Zhuang

Abstract

Summary. The paper gives first‐order residual analysis for spatiotemporal point processes that is similar to the residual analysis that has been developed by Baddeley and co‐workers for spatial point processes and also proposes principles for second‐order residual analysis based on the viewpoint of martingales. Examples are given for both first‐ and second‐order residuals. In particular, residual analysis can be used as a powerful tool in model improvement. Taking a spatiotemporal epidemic‐type aftershock sequence model for earthquake occurrences as the base‐line model, second‐order residual analysis can be useful for identifying many features of the data that are not implied in the base‐line model, providing us with clues about how to formulate better models.

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  • Jiancang Zhuang, 2006. "Second‐order residual analysis of spatiotemporal point processes and applications in model evaluation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 635-653, September.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:4:p:635-653
    DOI: 10.1111/j.1467-9868.2006.00559.x
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    Cited by:

    1. Yongtao Guan & Hansheng Wang, 2010. "Sufficient dimension reduction for spatial point processes directed by Gaussian random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 367-387, June.
    2. Reza Pourtaheri & Mohammad Vahidi-Asl, 2011. "Point pattern analysis of regional city distributions," Quality & Quantity: International Journal of Methodology, Springer, vol. 45(6), pages 1473-1481, October.
    3. Tonglin Zhang & Ge Lin, 2009. "Cluster Detection Based on Spatial Associations and Iterated Residuals in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 65(2), pages 353-360, June.
    4. Kieran Kalair & Colm Connaughton & Pierfrancesco Alaimo Di Loro, 2021. "A non‐parametric Hawkes process model of primary and secondary accidents on a UK smart motorway," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 80-97, January.
    5. repec:jss:jstsof:35:i08 is not listed on IDEAS
    6. Xin Chen & Jieli Ding & Liuquan Sun, 2018. "A semiparametric additive rate model for a modulated renewal process," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 675-698, October.
    7. Giada Adelfio & Frederic Schoenberg, 2009. "Point process diagnostics based on weighted second-order statistics and their asymptotic properties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 929-948, December.
    8. Fengchang Lin & Jason P. Fine, 2009. "Pseudomartingale estimating equations for modulated renewal process models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 3-23, January.

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