Spatial prediction in the presence of left-censoring

Environmental (spatial) monitoring of different variables often involves left-censored observations falling below the minimum detection limit (MDL) of the instruments used to quantify them. Several methods to predict the variables at new locations given left-censored observations of a stationary spatial process are compared. The methods use versions of kriging predictors, being the best linear unbiased predictors minimizing the mean squared prediction errors. A semi-naive method that determines imputed values at censored locations in an iterative algorithm together with variogram estimation is proposed. It is compared with a computationally intensive method relying on Gaussian assumptions, as well as with two distribution-free methods that impute the MDL or MDL divided by two at the locations with censored values. Their predictive performance is compared in a simulation study for both Gaussian and non-Gaussian processes and discussed in relation to the complexity of the methods from a user’s perspective. The method relying on Gaussian assumptions performs, as expected, best not only for Gaussian processes, but also for other processes with symmetric marginal distributions. Some of the (semi-)naive methods also work well for these cases. For processes with skewed marginal distributions (semi-)naive methods work better. The main differences in predictive performance arise for small true values. For large true values no difference between methods is apparent.