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Edge effects and efficient parameter estimation for stationary random fields. (English) Zbl 0633.62094

Edge effects are a serious problem in spatial statistics. Their importance increases with the dimension of a lattice in which a stationary random field is considered which parameters should be estimated. In estimating the covariances by the usual sum of products divided by the sample size there is a bias due to the boundary. Parameter estimation by minimizing the classical Whittle-approximation to the Gaussian log likelihood based on this covariance estimator is efficient only in one dimension.
The authors propose to modify this parameter estimation by introducing data tapers \[ h(u) = \begin{cases} w(2u/\rho) & (0\leq u<1/2\rho) \\ 1 & ((1/2)\rho\leq u\leq 1/2) \\ h(1-u) & (1/2<u\leq 1) \end{cases} \] with a continuous increasing function with \(w(0)=0\), \(w(1)=1\) and the smoothness parameter \(\rho\). The resulting modified estimators are efficient also in two and three dimensions.
Reviewer: D.Rasch

MSC:

62M99 Inference from stochastic processes
62F10 Point estimation
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