IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v36y2021i4d10.1007_s00180-021-01108-0.html
   My bibliography  Save this article

A computational validation for nonparametric assessment of spatial trends

Author

Listed:
  • A. Meilán-Vila

    (Universidade da Coruña)

  • R. Fernández-Casal

    (Universidade da Coruña)

  • R. M. Crujeiras

    (Universidade de Santiago de Compostela)

  • M. Francisco-Fernández

    (Universidade da Coruña)

Abstract

The analysis of continuously spatially varying processes usually considers two sources of variation, namely, the large-scale variation collected by the trend of the process, and the small-scale variation. Parametric trend models on latitude and longitude are easy to fit and to interpret. However, the use of parametric models for characterizing spatially varying processes may lead to misspecification problems if the model is not appropriate. Recently, Meilán-Vila et al. (TEST 29:728–749, 2020) proposed a goodness-of-fit test based on an $$L_2$$ L 2 -distance for assessing a parametric trend model with correlated errors, under random design, comparing parametric and nonparametric trend estimates. The present work aims to provide a detailed computational analysis of the behavior of this approach using different bootstrap algorithms for calibration, one of them including a procedure that corrects the bias introduced by the direct use of the residuals in the variogram estimation, under a fixed design geostatistical framework. Asymptotic results for the test are provided and an extensive simulation study, considering complexities that usually arise in geostatistics, is carried out to illustrate the performance of the proposal. Specifically, we analyze the impact of the sample size, the spatial dependence range and the nugget effect on the empirical calibration and power of the test.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01108-0
    DOI: 10.1007/s00180-021-01108-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-021-01108-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-021-01108-0?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. Shapiro, A. & Botha, J. D., 1991. "Variogram fitting with a general class of conditionally nonnegative definite functions," Computational Statistics & Data Analysis, Elsevier, vol. 11(1), pages 87-96, January.
    2. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 442-447, September.
    3. Crujeiras, Rosa M. & Van Keilegom, Ingrid, 2010. "Least squares estimation of nonlinear spatial trends," LIDAM Reprints ISBA 2010007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Castillo-Páez, Sergio & Fernández-Casal, Rubén & García-Soidán, Pilar, 2019. "A nonparametric bootstrap method for spatial data," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 1-15.
    5. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    6. 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.
    7. W. González-Manteiga & R. Cao, 1993. "Testing the hypothesis of a general linear model using nonparametric regression estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(1), pages 161-188, December.
    8. 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.
    9. Peter J. Diggle & Raquel Menezes & Ting‐li Su, 2010. "Geostatistical inference under preferential sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 191-232, March.
    10. J. Opsomer & M. Francisco-Fernández, 2010. "Finding local departures from a parametric model using nonparametric regression," Statistical Papers, Springer, vol. 51(1), pages 69-84, January.
    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. 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. Pedro H. C. Sant'Anna & Xiaojun Song & Qi Xu, 2022. "Covariate distribution balance via propensity scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1093-1120, September.
    3. Adam D. Bull, 2015. "Semimartingale detection and goodness-of-fit tests," Papers 1506.00088, arXiv.org, revised Jun 2016.
    4. Xu Guo & Gao-Rong Li & Michael McAleer & Wing-Keung Wong, 2018. "Specification Testing of Production in a Stochastic Frontier Model," Sustainability, MDPI, vol. 10(9), pages 1-10, August.
    5. 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.
    6. Enno Mammen & Jens Perch Nielsen & Michael Scholz & Stefan Sperlich, 2019. "Conditional Variance Forecasts for Long-Term Stock Returns," Risks, MDPI, vol. 7(4), pages 1-22, November.
    7. José María Sarabia & Faustino Prieto & Vanesa Jordá & Stefan Sperlich, 2020. "A Note on Combining Machine Learning with Statistical Modeling for Financial Data Analysis," Risks, MDPI, vol. 8(2), pages 1-14, April.
    8. Eduardo García‐Portugués & Javier Álvarez‐Liébana & Gonzalo Álvarez‐Pérez & Wenceslao González‐Manteiga, 2021. "A goodness‐of‐fit test for the functional linear model with functional response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 502-528, June.
    9. Junmin Liu & Deli Zhu & Luoyao Yu & Xuehu Zhu, 2023. "Specification testing of partially linear single-index models: a groupwise dimension reduction-based adaptive-to-model approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 232-262, March.
    10. Di Leo, Senatro & Caramuta, Pietro & Curci, Paola & Cosmi, Carmelina, 2020. "Regression analysis for energy demand projection: An application to TIMES-Basilicata and TIMES-Italy energy models," Energy, Elsevier, vol. 196(C).
    11. G. I. Rivas-Martínez & M. D. Jiménez-Gamero & J. L. Moreno-Rebollo, 2019. "A two-sample test for the error distribution in nonparametric regression based on the characteristic function," Statistical Papers, Springer, vol. 60(4), pages 1369-1395, August.
    12. Guo, Xu & Song, Lianlian & Fang, Yun & Zhu, Lixing, 2019. "Model checking for general linear regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 1-12.
    13. Zhou, Niwen & Guo, Xu & Zhu, Lixing, 2024. "Significance test for semiparametric conditional average treatment effects and other structural functions," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    14. Ioannis Kyriakou & Parastoo Mousavi & Jens Perch Nielsen & Michael Scholz, 2020. "Longer-Term Forecasting of Excess Stock Returns—The Five-Year Case," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    15. Wang, Tao, 2025. "Semi-functional varying coefficient mode-based regression," Journal of Multivariate Analysis, Elsevier, vol. 207(C).
    16. Colling, Benjamin & Van Keilegom, Ingrid, 2016. "Goodness-of-fit tests in semiparametric transformation models using the integrated regression function," LIDAM Discussion Papers ISBA 2016031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Scholz, Michael & Nielsen, Jens Perch & Sperlich, Stefan, 2015. "Nonparametric prediction of stock returns based on yearly data: The long-term view," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 143-155.
    18. Escanciano, Juan Carlos & Pardo-Fernandez, Juan Carlos & Van Keilegom, Ingrid, 2015. "Asymptotic distribution-free tests for semiparametric regressions," LIDAM Discussion Papers ISBA 2015001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Setareh Ranjbar & Stefan Sperlich, 2020. "A Note on Empirical Studies of Life-Satisfaction: Unhappy with Semiparametrics?," Journal of Happiness Studies, Springer, vol. 21(6), pages 2193-2212, August.
    20. Omid Bozorg-Haddad & Pouria Yari & Mohammad Delpasand & Xuefeng Chu, 2022. "Reservoir operation under influence of the joint uncertainty of inflow and evaporation," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 24(2), pages 2914-2940, February.

    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:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01108-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.