Supplementary materials for this article are available at https:// doi.org/ 10.1007/ s13253-018-0325-x .
The Use of Calibration Weighting for Variance
Estimation Under Systematic Sampling:
Applications to Forest Cover Assessment
Lorenzo Fattorini, Timothy G. Gregoire,andSaraTrentini
The purpose of this note is to propose a variance estimator under non-measurable
designs that exploits the existence of an auxiliary variable well correlated with the survey
variable of interest. Under non-measurable designs, the Sen–Yates–Grundy variance
estimator generates a downward bias that can be reduced using a calibration weighting
based on the auxiliary variable. Conditions of approximate unbiasedness for the resulting
calibration estimator are given. The application to systematic sampling is considered. The
proposal proves to be effective for estimating the variance of the forest cover estimator
in remote sensing-based surveys, owing to the strong correlation between the reference
data, available from a systematic sample, and the satellite map data, available for the
whole population and hence exploited as an auxiliary variable.
Supplementary materials accompanying this paper appear online.
Key Words: Calibration estimation; Forest cover estimation; Non-measurable designs;
Deforestation and forest degradation is one of the main causes of global greenhouse
gas emission. Reducing emission from deforestation and forest degradation (REDD) is a
United Nations project offering incentives to developing countries for reducing emissions
by increasing and improving forested lands. In this scenario, periodic and accurate forest
cover estimates are crucial (UN-REDD 2013). As large-scale ground surveys are impossible
in tropical and sub-tropical countries owing to high costs and forest inaccessibility, surveys
based on remote sensing imagery become mandatory.
Large-scale remote-sensing-based surveys are usually carried out by combining unsuper-
vised classiﬁcations of satellite imagery into forest/ non-forest categories with subsequent
visual on-screen enhancements taken as the ground truth (Hansen et al. 2013). Because
Lorenzo Fattorini (
)· Sara Trentini, Department of Economics and Statistics, University of Siena, Piazza S.
Francesco 8, 53100 Siena, Italy (E-mail: firstname.lastname@example.org). Timothy G. Gregoire, School of Forestry and
Environmental Studies, Yale University, 360 Prospect Street, New Haven, CT 06511-2104, USA.
© 2018 International Biometric Society
Journal of Agricultural, Biological, and Environmental Statistics