**Generalized regression estimator (GREG)**

Under a design-based approach for domain estimation, auxiliary data are usually incorporated in an estimation procedure by model-assisted techniques. Linear regression models are often adopted in the construction of generalized regression estimators (GREG; Särndal, et al. 1992; Estevao et al. 1995) that are design-unbiased. GREG estimators can often be expected to be precise especially for domains large enough but in the smallest domains, they tend to have large variance. Thus, small domains seem to call for model-dependent (or composite) estimators. See page 97 in Lehtonen, R & Pahkinen, E. (2004)