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Asymptotic normality of the Nadaraya–Watson semivariogram estimators

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Abstract

In this work, the Nadaraya–Watson semivariogram estimation is considered for both the isotropic and the anisotropic settings. Several properties of these estimators are analyzed and, particularly, their asymptotic normality is established in terms of unknown characteristics of the random process. The latter provides a theoretical procedure for construction of confidence intervals for the semivariogram via the normal quantiles, which in practice must be appropriately estimated. A numerical study is included to illustrate the performance of the Nadaraya–Watson estimation when used to obtain confidence intervals.

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Authors and Affiliations

  1. Facultad de Ciencias Sociales y de la Comunicación, Universidad de Vigo, Campus A Xunqueira, C.P. 36005, Pontevedra, Spain

    Pilar García-Soidán

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  1. Pilar García-Soidán
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Correspondence to Pilar García-Soidán.

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García-Soidán, P. Asymptotic normality of the Nadaraya–Watson semivariogram estimators. TEST 16, 479–503 (2007). https://doi.org/10.1007/s11749-006-0016-8

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  • DOI: https://doi.org/10.1007/s11749-006-0016-8

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