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Partial autocorrelation function for spatial processes. (English) Zbl 0806.62077
This paper deals with statistics of second-order stationary two- dimensional random fields. For data observed on a rectangular lattice, several authors suggested suitable two-dimensional ARMA models to apply time series methods. For a class of such ARMA-models a partial autocorrelation function (PACF) is defined and the estimation of this PACF is treated in detail. In case of Gaussian models some asymptotic properties are obtained. Their applicability in statistical analysis is discussed and partially supported by simulation studies.

MSC:
62M30 Inference from spatial processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M40 Random fields; image analysis
60F05 Central limit and other weak theorems
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