A statistical evaluation of non-ergodic variogram estimators

Geostatistics is a set of statistical techniques that is increasingly used to characterize spatial dependence in spatially referenced ecological data. A common feature of geostatistics is predicting values at unsampled locations from nearby samples using the kriging algorithm. Modeling spatial dependence in sampled data is necessary before kriging and is usually accomplished with the variogram and its traditional estimator. Other types of estimators, known as non-ergodic estimators, have been used in ecological applications. Non-ergodic estimators were originally suggested as a method of choice when sampled data are preferentially located and exhibit a skewed frequency distribution. Preferentially located samples can occur, for example, when areas with high values are sampled more intensely than other areas. In earlier studies the visual appearance of variograms from traditional and non-ergodic estimators were compared. Here we evaluate the estimators' relative performance in prediction. We also show algebraically that a non-ergodic version of the variogram is equivalent to the traditional variogram estimator. Simulations, designed to investigate the effects of data skewness and preferential sampling on variogram estimation and kriging, showed the traditional variogram estimator outperforms the non-ergodic estimators under these conditions. We also analyzed data on carabid beetle abundance, which exhibited large-scale spatial variability (trend) and a skewed frequency distribution. Detrending data followed by robust estimation of the residual variogram is demonstrated to be a successful alternative to the non-ergodic approach.     

Fitting Data to Linear Combinations of Covariograms

We pursue a regression model for spatially-indexed data whose spatial correlation is determined by a linear combination of simple covariograms. The main interest lies in the estimation of the spatial parameters. As several common techniques appear ineffective for this setting, an algorithm is proposed to obtain parameter estimates and is assessed through simulation. It is found to provide greater stability than other methods of estimation. We discuss the influence of parametrization and site location on the efficacy of the estimation algorithms, and develop some guidelines as to the placement of sampling sites to improve the algorithm's performance. This revised version was published online in July 2006 with corrections to the Cover Date.