{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:21:04Z","timestamp":1757618464163,"version":"3.44.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T00:00:00Z","timestamp":1750377600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T00:00:00Z","timestamp":1750377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100020619","name":"Universidad Miguel Hern\u00e1ndez","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100020619","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2025,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We introduce a novel nonparametric method for testing the hypothesis of independence between a marked point process with functional marks and a covariate. In a special case, when the functional marks are constructed using the local indicator of spatial association (LISA) functions, it results in testing the second-order intensity reweighted stationarity (SOIRS) hypothesis against a specific alternative that is determined by a chosen covariate. SOIRS is often used as a convenient assumption in analysing point patterns, but a general formal test of the SOIRS hypothesis is not available in the literature. Our simulation experiments indicate that the proposed test performs well both in size and power. The practical application of the proposed methodology is demonstrated using a point pattern of fish locations in a water reservoir, accompanied by four covariates.<\/jats:p>","DOI":"10.1007\/s11222-025-10669-9","type":"journal-article","created":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T09:39:50Z","timestamp":1750412390000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A nonparametric test of independence between the second-order structure of point patterns and covariates"],"prefix":"10.1007","volume":"35","author":[{"given":"Jonatan A.","family":"Gonz\u00e1lez","sequence":"first","affiliation":[]},{"given":"Ji\u0159\u00ed","family":"Dvo\u0159\u00e1k","sequence":"additional","affiliation":[]},{"given":"Tom\u00e1\u0161","family":"Mrkvi\u010dka","sequence":"additional","affiliation":[]},{"given":"Jorge","family":"Mateu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,6,20]]},"reference":[{"key":"10669_CR1","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1111\/j.1538-4632.1995.tb00338.x","volume":"27","author":"K Anselin","year":"1995","unstructured":"Anselin, K.: Local indicators of spatial association-LISA. Geogr. Anal. 27, 93\u2013115 (1995)","journal-title":"Geogr. Anal."},{"key":"10669_CR2","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1111\/1467-9574.00144","volume":"54","author":"A Baddeley","year":"2000","unstructured":"Baddeley, A., M\u00f8ller, J., Waagepetersen, R.: Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Stat. Neerl. 54, 329\u2013350 (2000)","journal-title":"Stat. Neerl."},{"key":"10669_CR3","doi-asserted-by":"publisher","DOI":"10.1201\/b19708","volume-title":"Spatial Point Patterns: Methodology and Applications with R","author":"A Baddeley","year":"2015","unstructured":"Baddeley, A., Rubak, E., Turner, R.: Spatial Point Patterns: Methodology and Applications with R. CRC Press, Boca Raton, Florida, Chapman & Hall Interdisciplinary Statistics Series (2015)"},{"key":"10669_CR4","doi-asserted-by":"publisher","DOI":"10.1002\/9781118136188","volume-title":"Geostatistics: Modeling Spatial Uncertainty","author":"JP Chil\u00e8s","year":"2012","unstructured":"Chil\u00e8s, J.P., Delfiner, P.: Geostatistics: Modeling Spatial Uncertainty, 2nd edn. Wiley Series in Probability and Statistics. John Wiley & Sons, Hoboken, New Jersey (2012)","edition":"2"},{"key":"10669_CR5","doi-asserted-by":"publisher","DOI":"10.1002\/9781118658222","volume-title":"Stochastic Geometry and Its Applications","author":"SN Chiu","year":"2013","unstructured":"Chiu, S.N., Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and Its Applications, 3rd edn. Wiley Series in Probability and Statistics. John Wiley & Sons, Chichester (2013)","edition":"3"},{"issue":"1","key":"10669_CR6","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1198\/108571101300325292","volume":"6","author":"N Cressie","year":"2001","unstructured":"Cressie, N., Collins, B.: Analysis of spatial point patterns using bundles of product density lisa functions. J. Agric. Biol. Environ. Stat. 6(1), 118\u2013135 (2001)","journal-title":"J. Agric. Biol. Environ. Stat."},{"key":"10669_CR7","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1002\/nav.1022","volume":"48","author":"N Cressie","year":"2001","unstructured":"Cressie, N., Collins, L.B.: Patterns in spatial point locations: local indicators of spatial association in a minefield with clutter. Nav. Res. Logist. 48, 333\u2013347 (2001)","journal-title":"Nav. Res. Logist."},{"key":"10669_CR8","unstructured":"Daley, D., Vere-Jones, D.: An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods (Second ed.). Springer-Verlag, New York (2003)"},{"key":"10669_CR9","doi-asserted-by":"publisher","DOI":"10.1201\/b15326","volume-title":"Statistical Analysis of Spatial and Spatio-Temporal Point Patterns","author":"PJ Diggle","year":"2013","unstructured":"Diggle, P.J.: Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, 3rd edn. CRC Press, Boca Raton, Florida, Chapman & Hall Monographs on Statistics & Applied Probability (2013)","edition":"3"},{"key":"10669_CR10","doi-asserted-by":"publisher","first-page":"100388","DOI":"10.1016\/j.spasta.2019.100388","volume":"33","author":"J Dvo\u0159\u00e1k","year":"2019","unstructured":"Dvo\u0159\u00e1k, J., M\u00f8ller, J., Mrkvi\u010dka, T., Soubeyrand, S.: Quick inference for log Gaussian Cox processes with non-stationary underlying random fields. Spatial Statistics 33, 100388 (2019)","journal-title":"Spatial Statistics"},{"issue":"3","key":"10669_CR11","doi-asserted-by":"publisher","first-page":"592","DOI":"10.1111\/insr.12503","volume":"90","author":"J Dvo\u0159\u00e1k","year":"2022","unstructured":"Dvo\u0159\u00e1k, J., Mrkvi\u010dka, T., Mateu, J., Gonz\u00e1lez, J.A.: Nonparametric testing of the dependence structure among points\u2013marks\u2013covariates in spatial point patterns. Int. Stat. Rev. 90(3), 592\u2013621 (2022)","journal-title":"Int. Stat. Rev."},{"issue":"3","key":"10669_CR12","doi-asserted-by":"publisher","first-page":"473","DOI":"10.2307\/1938452","volume":"68","author":"A Getis","year":"1987","unstructured":"Getis, A., Franklin, J.: Second-order neighborhood analysis of mapped point patterns. Ecology 68(3), 473\u2013477 (1987)","journal-title":"Ecology"},{"issue":"3","key":"10669_CR13","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1007\/s11749-020-00730-2","volume":"30","author":"M Ghorbani","year":"2021","unstructured":"Ghorbani, M., Cronie, O., Mateu, J., Yu, J.: Functional marked point processes: a natural structure to unify spatio-temporal frameworks and to analyse dependent functional data. TEST 30(3), 529\u2013568 (2021)","journal-title":"TEST"},{"issue":"4","key":"10669_CR14","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1007\/s13253-021-00455-1","volume":"26","author":"JA Gonz\u00e1lez","year":"2021","unstructured":"Gonz\u00e1lez, J.A., Rodr\u00edguez-Cort\u00e9s, F.J., Romano, E., Mateu, J.: Classification of events using local pair correlation functions for spatial point patterns. J. Agric. Biol. Environ. Stat. 26(4), 538\u2013559 (2021)","journal-title":"J. Agric. Biol. Environ. Stat."},{"key":"10669_CR15","doi-asserted-by":"crossref","unstructured":"Guan, Y., Jalilian, A., Waagepetersen, R.: Quasi-likelihood for spatial point processes. Journal of the Royal Statistical Society. Series B (Statistical Methodology)\u00a077(3): 677\u2013697 (2015)","DOI":"10.1111\/rssb.12083"},{"issue":"2","key":"10669_CR16","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1111\/sjos.12185","volume":"43","author":"U Hahn","year":"2016","unstructured":"Hahn, U., Vedel Jensen, E.B.: Hidden second-order stationary spatial point processes. Scand. J. Stat. 43(2), 455\u2013475 (2016)","journal-title":"Scand. J. Stat."},{"key":"10669_CR17","doi-asserted-by":"crossref","unstructured":"Illian, J., Penttinen, P., Stoyan, H., Stoyan, D.: Statistical Analysis and Modelling of Spatial Point Patterns. Statistics in Practice. Wiley (2008)","DOI":"10.1002\/9780470725160"},{"issue":"1","key":"10669_CR18","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/s10750-010-0398-1","volume":"654","author":"O Jarol\u00edm","year":"2010","unstructured":"Jarol\u00edm, O., Kube\u010dka, J., \u010cech, M., Va\u0161ek, M., Peterka, J., Mat\u011bna, J.: Sinusoidal swimming in fishes: the role of season, density of large zooplankton, fish length, time of the day, weather condition and solar radiation. Hydrobiologia 654(1), 253\u2013265 (2010)","journal-title":"Hydrobiologia"},{"issue":"1\/2","key":"10669_CR19","doi-asserted-by":"publisher","first-page":"81","DOI":"10.2307\/2332226","volume":"30","author":"MG Kendall","year":"1938","unstructured":"Kendall, M.G.: A new measure of rank correlation. Biometrika 30(1\/2), 81\u201393 (1938)","journal-title":"Biometrika"},{"key":"10669_CR20","doi-asserted-by":"crossref","unstructured":"Lotwick, H.W., Silverman, B.W.: Methods for analysing spatial processes of several types of points. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 44(3), 406\u2013413 (1982)","DOI":"10.1111\/j.2517-6161.1982.tb01221.x"},{"key":"10669_CR21","doi-asserted-by":"crossref","unstructured":"Lu, C., Guan, Y., van Lieshout, M.N.M., Xu, G.: XGBoostPP: Tree-based estimation of point process intensity functions (2024)","DOI":"10.1080\/10618600.2025.2520582"},{"issue":"3\u20134","key":"10669_CR22","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1002\/env.1028","volume":"21","author":"J Mateu","year":"2010","unstructured":"Mateu, J., Lorenzo, G., Porcu, E.: Features detection in spatial point processes via multivariate techniques. Environmetrics 21(3\u20134), 400\u2013414 (2010)","journal-title":"Environmetrics"},{"key":"10669_CR23","volume-title":"Statistical Inference and Simulation for Spatial Point Processes","author":"J M\u00f8ller","year":"2004","unstructured":"M\u00f8ller, J., Waagepetersen, R.P.: Statistical Inference and Simulation for Spatial Point Processes. CRC Press, Boca Raton, Florida, Chapman & Hall Monographs on Statistics & Applied Probability (2004)"},{"issue":"10","key":"10669_CR24","doi-asserted-by":"publisher","first-page":"1057","DOI":"10.1002\/sim.4160","volume":"30","author":"P Moraga","year":"2011","unstructured":"Moraga, P., Montes, F.: Detection of spatial disease clusters with lisa functions. Stat. Med. 30(10), 1057\u20131071 (2011)","journal-title":"Stat. Med."},{"issue":"1","key":"10669_CR25","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s11222-012-9355-3","volume":"24","author":"T Mrkvi\u010dka","year":"2014","unstructured":"Mrkvi\u010dka, T., Mu\u0161ka, M., Kube\u010dka, J.: Two step estimation for Neyman-Scott point process with inhomogeneous cluster centers. Stat. Comput. 24(1), 91\u2013100 (2014)","journal-title":"Stat. Comput."},{"key":"10669_CR26","doi-asserted-by":"publisher","first-page":"100430","DOI":"10.1016\/j.spasta.2020.100430","volume":"42","author":"T Mrkvi\u010dka","year":"2021","unstructured":"Mrkvi\u010dka, T., Dvo\u0159\u00e1k, J., Gonz\u00e1lez, J.A., Mateu, J.: Revisiting the random shift approach for testing in spatial statistics. Spatial Statistics 42, 100430 (2021)","journal-title":"Spatial Statistics"},{"issue":"1","key":"10669_CR27","first-page":"1","volume":"8","author":"M Mu\u0161ka","year":"2018","unstructured":"Mu\u0161ka, M., Tu\u0161er, M., Frouzov\u00e1, J., Mrkvi\u010dka, T., Ricard, D., Sed\u2019a, J., Morelli, F., Kube\u010dka, J.: Real-time distribution of pelagic fish: Combining hydroacoustics. GIS and spatial modelling at a fine spatial scale. 8(1), 1\u201311 (2018)","journal-title":"GIS and spatial modelling at a fine spatial scale."},{"key":"10669_CR28","doi-asserted-by":"crossref","unstructured":"Myllym\u00e4ki, M., Mrkvi\u010dka, T: GET: Global Envelopes in R. Journal of Statistical Software, 111(3), 1\u201340. (2024)","DOI":"10.18637\/jss.v111.i03"},{"issue":"2","key":"10669_CR29","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1111\/rssb.12172","volume":"79","author":"M Myllym\u00e4ki","year":"2017","unstructured":"Myllym\u00e4ki, M., Mrkvi\u010dka, T., Grabarnik, P., Seijo, H., Hahn, U.: Global envelope tests for spatial processes. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 79(2), 381\u2013404 (2017)","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"3","key":"10669_CR30","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1007\/s10463-016-0556-y","volume":"69","author":"M Proke\u0161ov\u00e1","year":"2017","unstructured":"Proke\u0161ov\u00e1, M., Dvo\u0159\u00e1k, J., Jensen, E.B.V.: Two-step estimation procedures for inhomogeneous shot-noise cox processes. Ann. Inst. Stat. Math. 69(3), 513\u2013542 (2017)","journal-title":"Ann. Inst. Stat. Math."},{"key":"10669_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/b98888","volume-title":"Functional Data Analysis","author":"JO Ramsay","year":"2005","unstructured":"Ramsay, J.O., Silverman, B.W.: Functional Data Analysis, 2nd edn. Springer Science & Business Media, New York (2005)","edition":"2"},{"key":"10669_CR32","doi-asserted-by":"publisher","first-page":"255","DOI":"10.2307\/3212829","volume":"13","author":"BD Ripley","year":"1976","unstructured":"Ripley, B.D.: The second-order analysis of stationary point processes. J. Appl. Probab. 13, 255\u2013266 (1976)","journal-title":"J. Appl. Probab."},{"issue":"2","key":"10669_CR33","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1111\/j.2517-6161.1977.tb01615.x","volume":"39","author":"BD Ripley","year":"1977","unstructured":"Ripley, B.D.: Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology) 39(2), 172\u2013212 (1977)","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"1","key":"10669_CR34","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1046\/j.1369-7412.2003.05343.x","volume":"66","author":"M Schlather","year":"2004","unstructured":"Schlather, M., Ribeiro, P.J., Diggle, P.J.: Detecting dependence between marks and locations of marked point processes. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 66(1), 79\u201393 (2004)","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"1\/2","key":"10669_CR35","doi-asserted-by":"publisher","first-page":"18","DOI":"10.2307\/2332526","volume":"36","author":"M Thomas","year":"1949","unstructured":"Thomas, M.: A generalization of Poisson\u2019s binomial limit for use in ecology. Biometrika 36(1\/2), 18\u201325 (1949)","journal-title":"Biometrika"},{"key":"10669_CR36","unstructured":"van der Vaart, A.W.: Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press (1998)"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10669-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-025-10669-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10669-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T20:54:09Z","timestamp":1757192049000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-025-10669-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,20]]},"references-count":36,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,10]]}},"alternative-id":["10669"],"URL":"https:\/\/doi.org\/10.1007\/s11222-025-10669-9","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"type":"print","value":"0960-3174"},{"type":"electronic","value":"1573-1375"}],"subject":[],"published":{"date-parts":[[2025,6,20]]},"assertion":[{"value":"27 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 June 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"133"}}