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.

This work describes the R package GET that implements global envelopes for a general set of d-dimensional vectors T in various applications. A 100(1 - α)% global envelope is a band bounded by two vectors such that the probability that T falls outside this envelope in any of the d points is equal to α. The term 'global' means that this probability is controlled simultaneously for all the d elements of the vectors. The global envelopes can be employed for central regions of functional or multivariate data, for graphical Monte Carlo and permutation tests where the test statistic is multivariate or functional, and for global confidence and prediction bands. Intrinsic graphical interpretation property is introduced for global envelopes. The global envelopes included in the GET package have this property, which particularly helps to interpret test results, by providing a graphical interpretation that shows the reasons of rejection of the tested hypothesis. Examples of different uses of global envelopes and their implementation in the GET package are presented, including global envelopes for single and several one- or two-dimensional functions, Monte Carlo goodness-of-fit tests for simple and composite hypotheses, comparison of distributions, functional analysis of variance, functional linear model, and confidence bands in polynomial regression.