Model-based prediction error uncertainty estimation for k-nn method

The k-nearest neighbour estimation method is one of the main tools used in multi-source forest inventories. It is a powerful non-parametric method for which estimates are easy to compute and relatively accurate. One downside of this method is that it lacks an uncertainty measure for predicted values and for areas of an arbitrary size. We present a method to estimate the prediction uncertainty based on the variogram model which derives the necessary formula for the k-nn method. A data application is illustrated for multi-source forest inventory data, and the results are compared at pixel level to the conventional RMSE method. We find that the variogram model-based method which is analytic, is competitive with the RMSE method.