A New Sampling Framework for Spatial Surveys with Application to the French National Forest Inventory.

This article focuses on the two-stage two-phase sampling design employed by the French National Forest Inventory (NFI) for spatial forest surveys. The method involves dividing the territory into a regular grid of cells, selecting a sample of cells in the first stage, and then randomly sampling points within these cells in the second stage; these points are classified using auxiliary information from photo-interpretation to guide a second-phase subsampling for field measurements. The study introduces a new theoretical framework for design-based inference combining finite and continuous population methods, proposes Horvitz–Thompson and post-stratified estimators with associated variance estimators, and evaluates their performance through a simulation study. Results indicate that the French NFI’s sampling strategy and proposed estimators provide effective and approximately unbiased estimates, with variance estimators being moderately conservative, and the framework is applicable to other forest and environmental surveys.