Finite population estimation under generalized linear model assistance

Finite population estimation is the overall goal of sample surveys. When information regarding auxiliary variables are available, one may take advantage of general regression estimators (GREG) to improve sample estimate precision. GREG estimators may be derived when the relationship between interest and auxiliary variables is represented by a normal linear model. However, in some scenarios, such as estimating class frequencies or counting process totals, Bernoulli or Poisson responses models are more suitable for describing the relationship between interest and auxiliary variables than normal linear model ones. This paper focuses on the general case for which the relationship between interest variables and the available auxiliary ones may be suitably described by a generalized linear model. The variable of interest’s finite population distribution is viewed in such scenario as if generated by an exponential family distribution, which includes Bernoulli, Poisson, Gamma and inverse Gaussian distributions. The resulting estimator is a generalized linear model regression estimator (GEREG). Its general form and basic statistical properties are presented and studied analytically and, empirically, through of Monte Carlo experiments. Three applications are presented in which the GEREG estimator shows better performance than GREG.