A functional regression model for inventories supported by aerial laser scanner data or photogrammetric point clouds

Forest inventories, with a probability sampling of a target variable Y and a potentially very large number of auxiliary variables (X) obtained from an aerial laser scanner or photogrammetry, are faced with the issue of model and variable selection when a model for linking Y to X is formulated. To bypass this step we propose a generic functional regression model (FRM) for use in both a design- and a model-based framework of inference. We demonstrate applications of FRM with inventory data from France, Germany, and Norway. The generic FRM achieved results that were comparable to those obtained with more traditional approaches based on model and variable selections. The proposed FRM generates interpretable regression coefficients and enables testing of practically relevant hypotheses regarding estimated models.