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A nonparametric bootstrap method for spatial data

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  • Castillo-Páez, Sergio
  • Fernández-Casal, Rubén
  • García-Soidán, Pilar

Abstract

The aim is to provide a nonparametric bootstrap method for spatial data, which can be either stationary or depart from the stationarity condition due to the presence of a non-constant trend. The proposed technique has been designed to reproduce the variability of the underlying process in an appropriate way, since it takes into account the bias effect due to the use of residuals. In certain cases, other approaches are applicable to spatial data, such as the block bootstrap, although they may fail, for instance, to provide an adequate inference on the variogram. There are also semiparametric resampling methods, based on factoring a parametric estimate of the covariance matrix. However, the results derived from them may be affected by a misspecification of the selected parametric model, as well as by the bias effect induced by the residuals on the estimation. The new procedure has been developed to overcome the aforementioned drawbacks, thus enabling its application to typical inference problems in geostatistics, such as those involving the trend or the second-order structure. The different bootstrap mechanisms have been compared in numerical studies designed to check their performance for a specific problem, namely, the approximation of the bias and the variance of two variogram estimators. In addition, a practical application of the new approach for inference on the variogram of precipitation data has also been included.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:137:y:2019:i:c:p:1-15
    DOI: 10.1016/j.csda.2019.01.017
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    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. Iranpanah, N. & Mohammadzadeh, M. & Taylor, C.C., 2011. "A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 578-587, January.
    3. Ricardo Cao, 1999. "An overview of bootstrap methods for estimating and predicting in time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 95-116, June.
    4. García-Soidán, Pilar H. & González-Manteiga, Wenceslao & Febrero-Bande, Manuel, 2003. "Local linear regression estimation of the variogram," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 169-179, August.
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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.

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