Some extensions of the classical GREG estimator in estimation for domains - ARCHIVED

"Classical GREG estimator" is used here to refer to the generalized regression estimator extensively discussed for example in Särndal, Swensson and Wretman (1992). This paper summarize some recent extensions of the classical GREG estimator when applied to the estimation of totals for population subgroups or domains. GREG estimation was introduced for domain estimation in Särndal (1981, 1984), Hidiroglou and Särndal (1985) and Särndal and Hidiroglou (1989), and was developed further in Estevao, Hidiroglou and Särndal (1995). For the classical GREG estimator, fixed-effects linear model serves as the underlying working or assisting model, and aggregate-level auxiliary totals are incorporated in the estimation procedure. In some recent developments, an access to unit-level auxiliary data is assumed for GREG estimation for domains. Obviously, an access to micro-merged register and survey data involves much flexibility for domain estimation. This view has been adopted for GREG estimation for example in Lehtonen and Veijanen (1998), Lehtonen, Särndal and Veijanen (2003, 2005), and Lehtonen, Myrskylä, Särndal and Veijanen (2007). These extensions cover the cases of continuous and binary or polytomous response variables, use of generalized linear mixed models as assisting models, and unequal probability sampling designs. Relative merits and challenges of the various GREG estimators will be discussed.