Note on the design-based estimation of densities, totals and goodness of fit in extensive inventories
Daniel Mandallaz · Repository for Publications and Research Data (ETH Zurich) · 2014
This note intends to clarify some per se elementary considerations about the estimation of densities, totals and goodness of fit in extensive inventories, which, rather surprisingly, do not seem to be common knowledge in the community of forest inventorists.The main difficulty is due to the fact that the forest area F is only part of a given territory F , e.g. the country or a region thereof, and that its exact delineation and surface area λ(F ) are usually unknown, in contrast to F .A common practice to bypass this problem is to estimate a spatial mean density for the variable of interest, e.g.timber volume, over F , and not over the forested area only, and to then multiply this mean density with the total surface area λ( F ).This note shows that this approach can be misleading for the assessment of goodness of fit R 2 in two-phase sampling and inefficient for the estimation of totals if p F = λ(F ) λ( F ) is small and the R 2 is large within F .The same holds for small-area estimation.