Spatio-Temporal Models in Small Area Estimation

Abstract

A spatial r egression model in a general mixed ef fects model framework has been proposed for the small ar ea estimation problem. A common a utocorrelation pa rameter across the small areas has r esulted in the improvement of the small area estimates. It has been found to be very useful in the cases where there is little improvement in the small area estimates due to the exogenous variables. A second or der approximation to the mean squared e rror (MSE) of the empirical be st linear unbiased predictor (EBLUP) has also been worked out. Using the Kalman filtering approach, a spatial temporal model has been proposed. I n this case also, a second order approximation to the MSE of the EBLUP has been obtained. A s a case study, the time series monthly per capita consumption expenditure (MPCE) data from the National Sa mple Survey Organisation (NSSO) of the Ministry of Statistics and Programme Implementation, Government of India, have been used for the validation of the models.