Semiparametric Filtering of Spatial Autocorrelation: The Eigenvector Approach

Abstract

IntroductionUsually we expect to see some degree of spatial autocorrelation among spatially distributed univariate observations. This autocorrelation originates from (a) missing exogenous factors that exhibit distinctive spatial patterns and thus spatially tie the residuals together or (b) underlying spatial processes that emerge from spatial exchange mechanisms among the observations, and/or (c) an inappropriate spatial aggregation of the underlying observational units (see Anselin, 1988;Tiefelsdorf, 2000). The presence of spatial autocorrelation violates the ordinarily stated assumption of stochastic independence among observations, on which statistical inference from most classical statistical models is based. Thus, ignoring spatial autocorrelation leads to biased standard errors and/or biased parameter estimates, as well as artificially inflated degrees of freedom (see Wakefield, 2003).Common practice, when dealing with spatially distributed observations, is to use either maximum likelihood estimation or Bayesian estimation. These parametric estimation procedures must explicitly specify the distributional characteristics of the underlying models. In contrast, nonparametric methods are distribution free without sacrificing too much information in a sample. However, they may become quite computer intensive. See Hollander and Wolfe (1999) for more details on nonparametric statistical methods. More specifically in the spatial domain, the nonparametric eigenvector filtering procedure does not require restrictive and perhaps unjustified distributional assumptions. The eigenvector spatial filtering procedure is founded on the standard ordinary least squares (OLS) estimator and is, apart from the assumptions of independence and constant variance of the disturbances, distribution free owing to the Gauss^Markov theorem. The spatial filtering estimator is fairly robust to model specification errors compared with a spatial maximum likelihood estimator. The interpretation of its results is straightforward as the different components of a spatial process can be

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