New regression estimators in forest inventories with two-phase sampling and partially exhaustive information: a design-based Monte Carlo approach with applications to small-area estimation

Abstract

We consider two-phase sampling schemes where one component of the auxiliary information is known in every point ("wall-to-wall") and a second component is available only in the large sample of the first phase, whereas the second phase yields a subsample with the terrestrial inventory. This setup is of growing interest in forest inventory thanks to the recent advances in remote sensing, in particular, the availability of LiDAR data. We propose a new two-phase regression estimator for global and local estimation and derive its asymptotic design-based variance. The new estimator performs better than the classical regression estimator. Furthermore, it can be generalized to cluster sampling and two-stage tree sampling within plots. Simulations and a case study with LiDAR data illustrate the theory.Résumé : Cet article propose un nouvel estimateur pour les inventaires forestiers utilisant des plans de sondage à deux phases pour lesquels l'information auxiliaire consiste en une première composante exhaustive connue en chaque point et une seconde composante connue seulement aux points du grand échantillon de la première phase. La deuxième phase consiste en un sous-échantillon des points de la première phase dans lesquels l'inventaire terrestre est effectué. Ce contexte est appelé à jour un rôle croissant grâce aux développements récents dans l'aquisition de données par télédétection. Nous proposons un nouvel estimateur par regression, aussi bien pour l'estimation globale que locale, et nous donnons sa variance asymptotique sous le plan de sondage. Le nouvel estimateur peut être adapté aux inventaire par satellites et avec tirage double des arbres au niveau de la placette terrestre. Un exemple utilisant des données LiDAR et des simulations illustrent la théorie. Le nouvel estimateur a de meilleures performance que l'estimateur de régression classique.

Multidimensional scaling of first-return airborne laser echoes for prediction and model-assisted estimation of a distribution of tree stem diameters

“…6). If a census of X is not available, but instead a large sample estimate of X, a model-assisted approach to inference is still possible with a few simple modifications (Mandallaz et al 2013;Ståhl et al 2016). Cited alternatives to MDS may claim a design-based empirical difference estimator (Baffetta et al 2009;Magnussen 2013) disregarding a critical requirement for predictions to be generated independently of the observed sample (Särndal et al 1992, ch.…”

A Double-Sampling Extension of the German National Forest Inventory for Design-Based Small Area Estimation on Forest District Levels

“…The estimators used in this study have been proposed by [25,30] and derive their mathematical properties under the so-called infinite population approach. Therefore, we shall first provide a short introduction into this general estimation framework.…”

“…Mandallaz [30] and Mandallaz et al [25] used this property particular for the case of small area estimation to derive better variance estimates based on the g-weight technique adapted from the works of Särndal et al [9]. In the following, we will give a short description of each small area estimator and refer to Mandallaz et al [25], Mandallaz [30], Mandallaz et al [35] if the reader requires additional mathematical details or proofs. The estimators have also been implemented in the open-source software-package forestinventory [36] in the statistical software R [37] which was used to compute all estimates in this study.…”

“…These models are trained using data from outside the small area in order to "borrow strength" from areas where information is available. Of numerous applications of SAE in forestry [22][23][24][25], most use unit-level models, i.e., the inventory plot is the unit of the response variable in the training data used for the model fit. Such unit-level models have been intensively investigated for timber volume estimation using various remote sensing auxiliary data [26,27].…”

“…Three types of model-assisted design-based small area regression estimators were used to derive point and variance estimates of mean standing timber volume for 45 and 405 forest management units on the two respective district levels. The SA-estimators we considered were the pseudo-small, extended pseudo-synthetic and the pseudo-synthetic design-based small area estimator suggested by Mandallaz [30] and Mandallaz et al [25]. Auxiliary data consisted of a canopy height model (CHM) obtained from a countrywide airborne laser scanning (ALS) and a tree species classification map to be used for regression within tree species strata.…”