Time series EBLUPS for small areas using survey data - ARCHIVED

In estimation for small areas it is common to borrow strength from other small areas since the direct survey estimates often have large sampling variability. A class of methods called composite estimation addresses the problem by using a linear combination of direct and synthetic estimators. The synthetic component is based on a model which connects small area means cross-sectionally (over areas) and/or over time. A cross-sectional empirical best linear unbiased predictor (EBLUP) is a composite estimator based on a linear regression model with small area effects. In this paper we consider three models to generalize the cross-sectional EBLUP to use data from more than one time point. In the first model, regression parameters are random and serially dependent but the small area effects are assumed to be independent over time. In the second model, regression parameters are nonrandom and may take common values over time but the small area effects are serially dependent. The third model is more general in that regression parameters and small area effects are assumed to be serially dependent. The resulting estimators, as well as some cross-sectional estimators, are evaluated using bi-annual data from Statistics Canada’s National Farm Survey and January Farm Survey.