Model-assisted forest inventory with parametric, semiparametric, and nonparametric models

Survey sampling with model-assisted estimation has been gaining popularity in forest inventory recently, as the availability of cheap, good-quality remotely sensed data that can be used as auxiliary information has improved. Most of the studies have been carried out using parametric (linear or nonlinear) models. However, nonparametric and semiparametric models such as k nearest neighbor, kernel, and generalized additive are widely used in forest inventory. The results are usually calculated using the difference estimator (i.e., assuming an external model), even though the models used are based on the sample (i.e., an internal model). In that case, variances will likely be underestimated. In this study, we analyze how well the difference estimator works for different types of models, both internal and external. The study is based on simulated populations produced using a C-vine copula model with empirical marginals. The external model is based on real data, and the internal models are estimated from samples from the simulated population. The results show that the analytical variance estimates for a difference estimator based on an overfitted kernel model can seriously underestimate the true variance.