IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v196y2023ics0047259x2300026x.html
   My bibliography  Save this article

Nonparametric testing for the specification of spatial trend functions

Author

Listed:
  • Zhang, Rongmao
  • Chan, Ngai Hang
  • Chi, Changxiong

Abstract

Correct specification of a spatial trend constitutes an important topic in statistics because it facilitates spatial kriging and inference. This paper proposes a global integrated squared error (GISE) statistics between the nonparametric smoothing surface and the parametric hypothesized model to test for the goodness-of-fit of spatial trends. By virtue of the m-dependence approximation of a stationary random field, it is shown that under certain regularity conditions, the proposed GISE statistics has an asymptotic normal distribution. Further, a grid-based block bootstrap (GBBB) procedure is also proposed to deal with the complicated asymptotic variance involved in the limit distribution. Numerical studies are also presented to illustrate the performance of the proposed method.

Suggested Citation

  • Zhang, Rongmao & Chan, Ngai Hang & Chi, Changxiong, 2023. "Nonparametric testing for the specification of spatial trend functions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:jmvana:v:196:y:2023:i:c:s0047259x2300026x
    DOI: 10.1016/j.jmva.2023.105180
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X2300026X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2023.105180?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410, June.
    2. Hallin, Marc & Lu, Zudi & Tran, Lanh T., 2004. "Kernel density estimation for spatial processes: the L1 theory," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 61-75, January.
    3. Daniel B. Neill, 2012. "Fast subset scan for spatial pattern detection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 337-360, March.
    4. Kaufman, Cari G. & Schervish, Mark J. & Nychka, Douglas W., 2008. "Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1545-1555.
    5. Stefanie Biedermann & Holger Dette, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 417-438, December.
    6. Zhenyu Jiang & Nengxiang Ling & Zudi Lu & Dag Tj⊘stheim & Qiang Zhang, 2020. "On bandwidth choice for spatial data density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 817-840, July.
    7. Faming Liang & Yichen Cheng & Qifan Song & Jincheol Park & Ping Yang, 2013. "A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 325-339, March.
    8. Lajos Horváth & Gregory Rice, 2015. "Testing Equality Of Means When The Observations Are From Functional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 84-108, January.
    9. Bin Chen & Yongmiao Hong, 2012. "Testing for Smooth Structural Changes in Time Series Models via Nonparametric Regression," Econometrica, Econometric Society, vol. 80(3), pages 1157-1183, May.
    10. Marc Hallin & Zudi Lu & Lanh T. Tran, 2001. "Density estimation for spatial linear processes," ULB Institutional Repository 2013/2109, ULB -- Universite Libre de Bruxelles.
    11. Bruce E. Hansen, 2001. "The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 117-128, Fall.
    12. El Machkouri, Mohamed & Volný, Dalibor & Wu, Wei Biao, 2013. "A central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 1-14.
    13. Liu, Weidong & Wu, Wei Biao, 2010. "Asymptotics Of Spectral Density Estimates," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1218-1245, August.
    14. Biedermann, Stefanie & Dette, Holger, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," Technical Reports 2000,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    15. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    16. Ingrid Keilegom & Wenceslao González Manteiga & César Sánchez Sellero, 2008. "Goodness-of-fit tests in parametric regression based on the estimation of the error distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 401-415, August.
    17. Ting Zhang & Wei Biao Wu, 2011. "Testing parametric assumptions of trends of a nonstationary time series," Biometrika, Biometrika Trust, vol. 98(3), pages 599-614.
    18. Likai Chen & Wei Biao Wu, 2019. "Testing for Trends in High-Dimensional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 869-881, April.
    19. Lahiri, S.N. & Robinson, Peter M., 2016. "Central limit theorems for long range dependent spatial linear processes," LSE Research Online Documents on Economics 65331, London School of Economics and Political Science, LSE Library.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Erhua Zhang & Xiaojun Song & Jilin Wu, 2022. "A non‐parametric test for multi‐variate trend functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 856-871, November.
    2. Degui Li & Bin Peng & Songqiao Tang & Weibiao Wu, 2023. "Inference of Grouped Time-Varying Network Vector Autoregression Models," Monash Econometrics and Business Statistics Working Papers 5/23, Monash University, Department of Econometrics and Business Statistics.
    3. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    4. Degui Li & Bin Peng & Songqiao Tang & Weibiao Wu, 2023. "Estimation of Grouped Time-Varying Network Vector Autoregression Models," Papers 2303.10117, arXiv.org, revised Mar 2024.
    5. Tang Qingguo, 2015. "Robust estimation for spatial semiparametric varying coefficient partially linear regression," Statistical Papers, Springer, vol. 56(4), pages 1137-1161, November.
    6. Gao, Jiti & Lu, Zudi & Tjostheim, Dag, 2003. "Estimation in semiparametric spatial regression," MPRA Paper 11979, University Library of Munich, Germany, revised Jul 2005.
    7. Xu Guo & Tao Wang & Lixing Zhu, 2016. "Model checking for parametric single-index models: a dimension reduction model-adaptive approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1013-1035, November.
    8. Xu Guo & Wangli Xu & Lixing Zhu, 2015. "Model checking for parametric regressions with response missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 229-259, April.
    9. Israel Martínez‐Hernández & Marc G. Genton, 2021. "Nonparametric trend estimation in functional time series with application to annual mortality rates," Biometrics, The International Biometric Society, vol. 77(3), pages 866-878, September.
    10. Chen, Likai & Wang, Weining & Wu, Wei Biao, 2019. "Inference of Break-Points in High-Dimensional Time Series," IRTG 1792 Discussion Papers 2019-013, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    11. Matthew J. Heaton & Abhirup Datta & Andrew O. Finley & Reinhard Furrer & Joseph Guinness & Rajarshi Guhaniyogi & Florian Gerber & Robert B. Gramacy & Dorit Hammerling & Matthias Katzfuss & Finn Lindgr, 2019. "A Case Study Competition Among Methods for Analyzing Large Spatial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 398-425, September.
    12. Kuangyu Wen & Ximing Wu & David J. Leatham, 2021. "Spatially Smoothed Kernel Densities with Application to Crop Yield Distributions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 349-366, September.
    13. Jenish, Nazgul, 2012. "Nonparametric spatial regression under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 167(1), pages 224-239.
    14. Anouar El Ghouch & Marc G. Genton & Taoufik Bouezmarni, 2013. "Measuring the Discrepancy of a Parametric Model via Local Polynomial Smoothing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 455-470, September.
    15. Chen, Bin, 2015. "Modeling and testing smooth structural changes with endogenous regressors," Journal of Econometrics, Elsevier, vol. 185(1), pages 196-215.
    16. Fu, Zhonghao & Hong, Yongmiao, 2019. "A model-free consistent test for structural change in regression possibly with endogeneity," Journal of Econometrics, Elsevier, vol. 211(1), pages 206-242.
    17. Mohamed El Machkouri, 2011. "Asymptotic normality of the Parzen–Rosenblatt density estimator for strongly mixing random fields," Statistical Inference for Stochastic Processes, Springer, vol. 14(1), pages 73-84, February.
    18. Amiri, Aboubacar & Dabo-Niang, Sophie, 2018. "Density estimation over spatio-temporal data streams," Econometrics and Statistics, Elsevier, vol. 5(C), pages 148-170.
    19. Bücher, Axel & Dette, Holger & Wieczorek, Gabriele, 2011. "Testing model assumptions in functional regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1472-1488, November.
    20. Sun, Yuying & Hong, Yongmiao & Lee, Tae-Hwy & Wang, Shouyang & Zhang, Xinyu, 2021. "Time-varying model averaging," Journal of Econometrics, Elsevier, vol. 222(2), pages 974-992.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:196:y:2023:i:c:s0047259x2300026x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.