This study adds to our ability to predict the unknown by empirically assessing the performance of a novel geostatistical-nonparametric hybrid technique to provide accurate predictions of the value of an attribute together with locally-relevant measures of prediction confidence, at point locations for a single realisation spatial process. The nonstationary variogram technique employed generalises a moving window kriging (MWK) model where classic variogram (CV) estimators are replaced with information-rich, geographically weighted variogram (GWV) estimators. The GWVs are constructed using kernel smoothing. The resultant and novel MWK-GWV model is compared with a standard MWK model (MWK-CV), a standard nonlinear model (Box-Cox kriging, BCK) and a standard linear model (simple kriging, SK), using four example datasets. Exploratory local analyses suggest that each dataset may benefit from a MWK application. This expectation was broadly confirmed once the models were applied. Model performance results indicate much promise in the MWK-GWV model. Situations where a MWK model is preferred to a BCK model and where a MWK-GWV model is preferred to a MWK-CV model are discussed with respect to model performance, parameterisation and complexity; and with respect to sample scale, information and heterogeneity.