A comparison of plug-in predictors for lognormal kriging

When skewed spatial data are encountered, a common procedure is to invoke lognormal kriging. The resultant naïve lognormal predictors are however biased. A family of optimal predictors which address this unbiasedness has been introduced into the literature by De Oliveira (2006). The behaviour of this family is well documented in the case of known covariance parameters. In contrast, when the covariance parameters are not known and must be estimated, the behaviour of the predictors is unknown. In the present paper, the performance of a subset of the family of predictors formulated by De Oliveira (2006), together with a predictor introduced by Abt et al. (1999), with ‘plug-in’ estimates of the covariance parameters introduced into the appropriate theoretical formulae, is investigated by means of a simulation study. Results based on eighteen scenarios describing a range of covariance structures and three performance criteria are presented and, in addition, results for a real world example are reported. The main features to emerge from the study are that the naïve predictor is negatively biased, that the lognormal predictor is representative of key predictors in the class introduced by De Oliveira (2006) and that the empirical mean squared prediction error severely underestimates the true value.