Precision of exogenous post-stratification in small-area estimation based on a continuous national forest inventory

Abstract

National forest inventories (NFIs) are designed to provide accurate information on forest resources at the national and regional levels, but there is also a demand for such information at smaller spatial scales. Auxiliary data such as satellite imagery have been used to facilitate small-area estimation. The commonly used method, k-nearest neighbour (k-NN), provides a model-based estimator for small areas, but a design-unbiased estimator for the mean square error is not available. Post-stratification (PS) is an alternative approach to using auxiliary information that allows for design-based variance estimation. In a case study using real inventory data of the Finnish NFI, we applied this method to the municipality level to explore the lower limit to the area for which the key forest parameters, forest area and growing stock volumes, can be estimated with sufficient precision. For PS, we employed exogenous forest resources maps based on the previous NFI round. In the municipalities of the two study provinces, the relative standard errors of total volume estimates ranged from 2.3% to 26.9%. They were smaller than 10% for municipalities with an area of 390 km2 or larger, corresponding to approximately 100 or more sample plots on forestland. We also demonstrated the usefulness of design-unbiased variance estimation in showing discrepancies between design-based PS and model-based k-NN estimates.

National mapping and estimation of forest area by dominant tree species using Sentinel-2 data

“…Improvements of national-scale estimates using remotely-sensed data are rarely reported. However, similar observations in the present study were made for example by Haakana et al (2020) on the level of municipalities. They used poststratification based on the Finnish multisource national forest inventory to estimate forest characteristics for municipalities and report clear improvements compared to direct estimates.…”

“…Gjertsen 2007), if mapping errors cannot be corrected (Tomppo et al 2009). Poststratification (Katila et al 2000, Haakana et al 2020 or model-assisted estimation (McRoberts et al 2010) may in such cases be better alternatives that also provide estimates of uncertainty.…”

A Systematic Review of Small Domain Estimation Research in Forestry During the Twenty-First Century From Outside the United States

“…The emergence of journal policies to publish accepted journal on-line prior to articles appearing in printed volumes often results in two different years for citations. For example, Haakana et al (2019b) was published on-line on 10 December 2019 but didn't appear in print until the April 2020 issue. The citations in this article use the on-line publication date rather than the in-print date.…”

“…Further, the small area estimates from post-stratification were robust compared to the field plot data estimates because the largest variances improved more than the average variances. Haakana et al (2019b) acknowledged that the k-NN method can provide a model-based estimator for small geographic areas, but not a designed-unbiased estimator for RMSE. Thus, in this article they focused specifically on municipalities to explore the lower limits in geographic size that could still yield estimates of forest area and growing stock volume with adequate precision.…”

Small Area Estimation of Postfire Tree Density Using Continuous Forest Inventory Data

“…More generally, drawing data from outside the domain of interest but from regions that share other characteristics (e.g., ecological subsection) has parallels in the ideas underlying post-stratification. Yet post-stratified estimation is most commonly implemented as a strictly direct estimation approach (e.g., Haakana et al 2020) without drawing on data from strata that extend beyond the domain of interest.…”