Abstract

Model-based small area estimation methods based on implicit or explicit models are extensively applied to produce precise estimates using additional information from related areas. The widely used Fay–Herriot model assumes that area-specific direct survey estimates follow an area-level linear mixed model with area as uncorrelated random effects. When available, historical data offer valuable information that can be used to improve estimators at the current instant; that is, it is also possible to borrow strength from time. The Fay–Herriot model does not allow for time variation in the area characteristics that is not explained by the auxiliary variables. Apart from making use of historical data and including the temporal correlation in the model, it is well known that when there is unexplained spatial correlation in the data, not considering it in the model will lead to erroneous inferences. A spatio-temporal version of the multivariate Fay–Herriot model is introduced. The residual maximum likelihood (REML) is described for parameter estimation, and empirical best linear unbiased predictors are derived under the proposed model. To measure the uncertainty of the proposed predictor, analytical and bootstrap-based mean squared error (MSE) estimation methods are also developed. Through a number of simulation studies, the performance of the proposed predictor along with the MSE estimators is evaluated. The findings evidently show that the proposed predictor outperforms the existing predictors. Both proposed MSE estimators track the actual value of MSE reasonably well, with confidence intervals based on them achieving close to nominal coverage. An application has also been made using the proposed methodology to estimate district-level food insecurity in the state of Bihar using the latest available data from the Household Consumer Expenditure Survey 2023-24 of India. The findings are expected to offer key insights to policymakers in identifying areas that required more attention.