Model Based Thin-plate Smoothing
نویسنده
چکیده
This paper presents a nonstationary structural spatial model that explicitly sets the data to evolve across a rectangular lattice constrained by secondorder smoothing restrictions. The model exemplifies the concept of model-based spatial smoothing and, in particular, it provides a rationale for the popular discrete thin-plate smoothing method. We show how to use a frequency-domain approach in order to estimate the spatial model via maximum likelihood. In essence, the approach allows both dimensions to be treated separately from each other so that the computational burden associated with the estimation of two-dimensional models is dramatically reduced both in terms of computing time and memory size. Besides, this spectral approach allows straightforward construction of analytic derivatives and an expression for the asymptotic variance of the estimated smoothing parameter is derived with which to construct confidence intervals. Some numerical evidence illustrate the results given.
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