, Volume 16, Issue 3, pp 479–503 | Cite as

Asymptotic normality of the Nadaraya–Watson semivariogram estimators

Original Paper


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.


Asymptotic normality Intrinsic stationarity Isotropy Kernel Random process Variogram 

Mathematics Subject Classification (2000)

62G05 62G10 


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2007

Authors and Affiliations

  1. 1.Facultad de Ciencias Sociales y de la ComunicaciónUniversidad de VigoPontevedraSpain

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