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    A Monte Carlo-adjusted goodness-of-fit test for parametric models describing spatial point patterns

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    Type
    Article
    Authors
    Dao, Ngocanh
    Genton, Marc G. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Spatio-Temporal Statistics and Data Analysis Group
    Statistics Program
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2014-04-28
    Online Publication Date
    2014-04-28
    Print Publication Date
    2014-04-03
    Permanent link to this record
    http://hdl.handle.net/10754/563485
    
    Metadata
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    Abstract
    Assessing the goodness-of-fit (GOF) for intricate parametric spatial point process models is important for many application fields. When the probability density of the statistic of the GOF test is intractable, a commonly used procedure is the Monte Carlo GOF test. Additionally, if the data comprise a single dataset, a popular version of the test plugs a parameter estimate in the hypothesized parametric model to generate data for theMonte Carlo GOF test. In this case, the test is invalid because the resulting empirical level does not reach the nominal level. In this article, we propose a method consisting of nested Monte Carlo simulations which has the following advantages: the bias of the resulting empirical level of the test is eliminated, hence the empirical levels can always reach the nominal level, and information about inhomogeneity of the data can be provided.We theoretically justify our testing procedure using Taylor expansions and demonstrate that it is correctly sized through various simulation studies. In our first data application, we discover, in agreement with Illian et al., that Phlebocarya filifolia plants near Perth, Australia, can follow a homogeneous Poisson clustered process that provides insight into the propagation mechanism of these plants. In our second data application, we find, in contrast to Diggle, that a pairwise interaction model provides a good fit to the micro-anatomy data of amacrine cells designed for analyzing the developmental growth of immature retina cells in rabbits. This article has supplementary material online. © 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
    Citation
    Dao, N. A., & Genton, M. G. (2014). A Monte Carlo-Adjusted Goodness-of-Fit Test for Parametric Models Describing Spatial Point Patterns. Journal of Computational and Graphical Statistics, 23(2), 497–517. doi:10.1080/10618600.2012.760459
    Sponsors
    This publication is based in part on work supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST) and by NSF grants DMS-1007504 and DMS-1106494. The authors thank the editor, the associate editor, and a referee for their helpful comments and suggestions. The first author thanks Dr. Naisyin Wang for suggesting the topic of this article. The authors also acknowledge the Texas A&M University Brazos HPC cluster that contributed to the research reported here.
    Publisher
    Informa UK Limited
    Journal
    Journal of Computational and Graphical Statistics
    DOI
    10.1080/10618600.2012.760459
    ae974a485f413a2113503eed53cd6c53
    10.1080/10618600.2012.760459
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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