A three-phase sampling extension of the generalized regression estimator with partially exhaustive information

Abstract

We consider three-phase sampling schemes in which one component of the auxiliary information is known in the very large sample of the so-called null phase and the second component is available only in the large sample of the first phase, whereas the second phase provides the terrestrial inventory data. We extend to three-phase sampling the generalized regression estimator that applies when the null phase is exhaustive, for global and local estimation, and derive its asymptotic design-based variance. The new three-phase regression estimator is particularly useful for reducing substantially the computing time required to treat exhaustively very large data sets generated by modern remote sensing technology such as LiDAR.