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Least squares estimation of nonlinear spatial trends

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  • 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
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    References listed on IDEAS

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    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.
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    1. 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.
    2. 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.
    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.

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