Comparison of classical, kernel-based, and nearest neighbors regression estimators using the design-based Monte Carlo approach for two-phase forest inventories

Abstract

This paper compares design-based properties of the classical two-phase regression estimator with several nonparametric kernel-based estimators of which k nearest neighbors (kNN) is a special case. Metrics are based on the Euclidean distance applied to either a multidimensional space of explanatory variables or to a one-dimensional space of predictions obtained from a linear model. The main concepts of kernel-based regression estimators are reformulated in the design-based Monte Carlo approach to forest inventory. The results, based on a case study of a forest inventory in Switzerland and extensive simulations, suggest that the commonly used analytical external variance formula may systematically underestimate the true variance for a variety of kernel-based estimators including kNN but that it is still adequate for the classical regression estimator. Although using a bootstrap variance can help to correct this underestimation, it was also found that the bootstrap variance estimates could be unstable if the optimal bandwidth is recalculated in each bootstrap sample. These findings suggest that if the model captures the main features of the underlying process, then it is advisable to use the classical regression estimator, because it performs at least as well as the other techniques and is by far simpler to implement.