IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i2p452-465.html

Least squares estimation of nonlinear spatial trends

Author

Listed:
  • Crujeiras, Rosa M.
  • Van Keilegom, Ingrid

Abstract

Results on asymptotic and finite sample properties of an estimator of a nonlinear regression function when errors are spatially correlated, and when the spatial dependence structure is unknown are derived. The proposed method is based on a generalized nonlinear least squares approach, taking into account the spatial covariance. Weak consistency of the regression parameters estimator is derived, along with its asymptotic Gaussian limit. The behavior of the proposed estimator is illustrated with a simulation study, considering different correlation structures in and a more general case including a spatial covariate. The method is also applied to two real data cases.

Suggested Citation

  • Crujeiras, Rosa M. & Van Keilegom, Ingrid, 2010. "Least squares estimation of nonlinear spatial trends," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 452-465, February.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:452-465
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(09)00330-2
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Hyon‐Jung Kim & Dennis D. Boos, 2004. "Variance Estimation in Spatial Regression Using a Non‐parametric Semivariogram Based on Residuals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 387-401, September.
    2. Fuentes, Montserrat, 2005. "A formal test for nonstationarity of spatial stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 30-54, September.
    3. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andrea Meilán-Vila & Jean D. Opsomer & Mario Francisco-Fernández & Rosa M. Crujeiras, 2020. "A goodness-of-fit test for regression models with spatially correlated errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 728-749, September.
    2. A. Meilán-Vila & R. Fernández-Casal & R. M. Crujeiras & M. Francisco-Fernández, 2021. "A computational validation for nonparametric assessment of spatial trends," Computational Statistics, Springer, vol. 36(4), pages 2939-2965, December.
    3. Jonathan Acosta & Felipe Osorio & Ronny Vallejos, 2016. "Effective Sample Size for Line Transect Sampling Models with an Application to Marine Macroalgae," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 407-425, September.

    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. Bowman, Adrian W. & Crujeiras, Rosa M., 2013. "Inference for variograms," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 19-31.
    2. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org, revised Aug 2022.
    3. Nadiezhda de la Uz, 2002. "La hipótesis de martingala en el mercado bursátil mexicano," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 17(1), pages 91-127.
    4. Niels Lundtorp Olsen & Alessia Pini & Simone Vantini, 2021. "False discovery rate for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 784-809, September.
    5. Arie Preminger & Uri Ben-zion & David Wettstein, 2007. "The extended switching regression model: allowing for multiple latent state variables," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(7), pages 457-473.
    6. Andreasen, Martin M. & Christensen, Bent Jesper, 2015. "The SR approach: A new estimation procedure for non-linear and non-Gaussian dynamic term structure models," Journal of Econometrics, Elsevier, vol. 184(2), pages 420-451.
    7. Corradi, Valentina & Fosten, Jack & Gutknecht, Daniel, 2024. "Predictive ability tests with possibly overlapping models," Journal of Econometrics, Elsevier, vol. 241(1).
    8. Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Value at Risk by Quantile Regression," NBER Working Papers 7341, National Bureau of Economic Research, Inc.
    9. Myoungji Lee & Marc G. Genton & Mikyoung Jun, 2016. "Testing Self-Similarity Through Lamperti Transformations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 426-447, September.
    10. Jonah B. Gelbach & Doug Miller, 2009. "Robust Inference with Multi-way Clustering," Working Papers 226, University of California, Davis, Department of Economics.
    11. repec:ebl:ecbull:v:3:y:2005:i:29:p:1-10 is not listed on IDEAS
    12. Su, Liangjun & Jin, Sainan, 2012. "Sieve estimation of panel data models with cross section dependence," Journal of Econometrics, Elsevier, vol. 169(1), pages 34-47.
    13. A. Colin Cameron & Douglas L. Miller, 2010. "Robust Inference with Clustered Data," Working Papers 106, University of California, Davis, Department of Economics.
    14. Shaw, Kathryn L, 1996. "An Empirical Analysis of Risk Aversion and Income Growth," Journal of Labor Economics, University of Chicago Press, vol. 14(4), pages 626-653, October.
    15. MacKinnon, James G., 2011. "Thirty Years of Heteroskedasticity-Robust Inference," Queen's Economics Department Working Papers 273816, Queen's University - Department of Economics.
    16. Kozhan, Roman & Salmon, Mark, 2009. "Uncertainty aversion in a heterogeneous agent model of foreign exchange rate formation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1106-1122, May.
    17. Rappoport, Peter & White, Eugene N., 1993. "Was There a Bubble in the 1929 Stock Market?," The Journal of Economic History, Cambridge University Press, vol. 53(3), pages 549-574, September.
    18. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    19. Ferreira, Eva & Gil-Bazo, Javier & Orbe, Susan, 2008. "Nonparametric estimation of conditional beta pricing models," DEE - Working Papers. Business Economics. WB wb082403, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    20. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.

    More about this item

    Statistics

    Access and download statistics

    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:csdana:v:54:y:2010:i:2:p:452-465. 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/locate/csda .

    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.