A matching procedure to improve k-NN estimation of forest attribute maps

The integration of forest inventory and mapping has emerged as a major issue for assessing forest attributes and multiple environmental functions. Associations between remotely sensed data and the biophysical attributes of forest vegetation (standing wood volume, biomass increment, etc.) can be exploited to estimate the attribute values for sampled and non-sampled pixels, thus producing maps for the entire region of interest. Among the available procedures, the k-nearest neighbours (k-NN) technique is becoming popular, even for practical applications. However, the k-NN estimates at the pixel level tend to average towards the population mean and to have suppressed variance, since large values are usually underestimated and small values overestimated. This tendency may be detrimental for k-NN applications in forest resource management planning and scenario analysis where the representation of the spatial variability of each attribute of interest across the surveyed territory is fundamental. The present paper proposes a procedure to tackle such an issue by modifying k-NN estimates via a post-processing procedure of distribution matching. The empirical distribution function of the population values is estimated from the sample of ground data by using the 0-inflated beta distribution as the assisting model and the k-NN estimates are subsequently modified in such a way as to match the estimated distribution. The statistical properties of the distribution matching estimators for totals and averages are theoretically derived, while the performance of the distribution matching estimator at the pixel level are empirically evaluated by a simulation study.