Borrowing strength from past data in small domain prediction by kalman filtering - a case

Point and interval estimators for small domains based exclusively on current and domain specific sample observations are generally ineffective because of inadequate sample-sizes. So, borrowing strength from sample values for analogous domains and simultaneously from all relevant past and auxiliary data is useful in deriving improved small domain statistics. Postulating for simplicity a linear regression model with a single covariate and a zero intercept but a time-specific domain-invariant slope we start with “synthetic” generalized regression predictors for the domain totals. These borrow across only domains. For further improvements a simple autoregressive model is postulated for the slope parameters. Employing Kalman filtering the previous predictors are revised to borrow supplementary strength across time. As drastic simplifying assumptions are needed in such predictions the efficacy of the procedure is examined through an empirical exercise using live data as well as simulations. The numerical findings turn out encouraging.