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)
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Hall P, Fisher NI, Hoffmann B (1994) On the nonparametric estimation of covariance functions. Ann Stat 22:2115–2134
Hall P, Patil P (1994) Properties of nonparametric estimators of autocovariance for stationary random fields. Probab Theory Relat Fields 99:399–424
Lahiri SN, Lee Y, Cressie N (2002). On asymptotic distribution and asymptotic efficiency of least squares estimators of spatial variogram parameters. J Stat Plan Inference 103:65–85