Design-based diagnostics for k-NN estimators of forest resources

Abstract

The k-nearest neighbours (k-NN) method constitutes a possible approach to improve the precision of the Horvitz– Thompson estimator of a single interest variable using auxiliary information at the estimation stage. Improvements are likely to occur when the neighbouring structure in the space of auxiliary variables is similar to the neighbouring structure in the space of the survey variables. Populations suitable for k-NN can be identified via the scores of the first principal component computed on the variance–covariance matrix of auxiliary variables. If the first principal component explains a large portion of the whole variability, distances among scores provide good approximations of distances in the space of auxiliary variables in such a way that the effectiveness of k-NN can be assessed by plotting the first principal component scores versus the sampled values of each of the interest variables. Monotone relationships with high values of Spearman’s correlation coefficients should denote effectiveness. Otherwise, when the first principal component explains small fractions of the total variation, an index that directly quantifies the similarity between the neighbouring structure in the space of interest and auxiliary variables is proposed. The validity of the proposed diagnostics is theoretically argued and empirically proven by a simulation study performed on a wide range of artificial and real populations.