Nonparametric methods especially kernel method is extensively used in model identification, diagnostic checking, and forecasting. For dealing with spatial cases the usage of these methods is not that common. One major reason for this is that, the sampling points are not evenly spaced. Time series observations are aggregated at regular intervals. But physical constraints measurement points may not be at regular intervals. Because of this spatial analysis is handled mostly by parametric models. Yet another reason is that mostly linear models are used for spatial analysis though conjugative kriging models are nonlinear. When observations are not taken in the regular intervals means there may not be enough points to estimate the joint density for all time periods concerned. The situation is more complicated for spatial case. Thus non-parametric procedure has been developed exclusively for spatial data. This article constructs an asymptotic theory for nonparametric marginal and joint density estimations for a random field with irregularly placed data points. (53 refs.)
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