Variance estimation for mean growth from successive double sampling for stratification

Abstract

Double sampling for stratification (2SS) is a sampling design that is widely used for forest inventories. We present the mathematical derivation of two appropriate variance estimators for mean growth from repeated 2SS with updated stratification on each measurement occasion. Both estimators account for substratification based on the transition of sampling units among the strata due to the updated allocation. For the first estimator, sizes of the substrata were estimated from the second-phase sample (sample plots), whereas the respective sizes in the second variance estimator relied on the larger first-phase sample. The estimators were empirically compared with a modified version of Cochran’s well-known 2SS variance estimator that ignores substratification. This was done by performing bootstrap resampling on data from two German forest districts. The major findings were as follows: (i) accounting for substratification, as implemented in both new estimators, has substantial impact in terms of significantly smaller variance estimates and bias compared with the estimator without substratification, and (ii) the second estimator with substrata sizes being estimated from the first-phase sample shows a smaller bias than the first estimator.